1) St. Clement: The third successor to St. Peter restored deposed presbyters in the Church at Corinth (Greece), stating: “If anyone disobey the things which have been said by [the Holy Spirit] through us [i.e., Rome], let them know that they will involve themselves in transgression and no small danger” (Letter to the Corinthians [ca. 80/96 AD]).
2) St. Ignatius of Antioch singled out Rome for special honor, writing that it held the “presidency of love” (Letter to the Romans [ca. 105 AD]).
3) St. Irenaeus: ca. 200 AD]). Of course, nothing prevents a double meaning in the passage (i.e., the rock can also be seen as Peter’s confession), but the primary meaning is undoubtedly Peter himself.

St. Clement of Alexandria refers to Peter as “the chosen, the preeminent, the first among the disciples” (Who is the Rich Man that is Saved? [190/210 AD]).
9) The Letter of Clement to James (221 AD) refers to Peter as “the foundation of the Church.”
10) Origen wrote that Peter was “the great foundation of the Church, that most solid of rocks, upon whom Christ built the Church” (Homilies on Exodus [after 244 AD]).
11) St. Cyprian wrote extensively about the Roman primacy, saying that “false faith can have no access” to Rome and that “sacerdotal unity has its source [in] the chair of Peter” (Letter [252 AD]).
12) Poem Against the Marcionites (267 AD): “In this chair in which he himself had sat, Peter, in mighty Rome, commanded Linus, the first elected, to sit down . . .”
13) St. Peter of Alexandria referred to Peter as “the first chosen of the Apostles” (Penance [306 AD]).
14) As far as I know, every bishop of Rome up through Constantine’s legalization of Christianity in 313 AD was martyred for the faith. In other words, to be consecrated bishop of Rome was tantamount to a death sentence for Christianity’s first three centuries. After Constantine, the popes were able to come out of hiding in the catacombs and fully become what Christ intended. Relatedly, the United States today looks nothing like it did in 1787, when it ratified our Constitution. Should it come as a surprise that the Catholic Church looked different in the 5th century than in the 1st century? Certainly not.
15) Pope St. Julius rebuked Alexandria for deposing St. Athanasius without first consulting Rome, grounding his rebuke on an earlier custom of the church. He assumed he had the authority to reopen cases which had already been closed in other apostolic sees (Letter [341 AD]).
16) St. Athanasius: “When I left Alexandria, I did not go to your brother’s headquarters, or to any other persons, but only to Rome; and having my case before the Church, I spent my time in the public worship” (Letter to Emperor Constantius).
17) Council of Sardica, canon 3 (342 AD): “But if any bishop loses the judgment in some case, and still believes that he has not a bad but a good case, in order that the case may be judged anew, if it pleases Your Charities, let us honor the memory of the Apostle Peter, by having those who gave the judgment write to Julius, Bishop of Rome, so that, if it seem proper, he may himself send arbiters, and judgment may be made again by the bishops of a neighboring province.”
18) St. Ephraim wrote that Jesus made Peter “the foundation of the holy Church” (Homilies [351 AD]).
19) St. Cyril of Jerusalem stated that Peter was the “chief” and the “first and foremost of the Apostles” (Catechetical Lectures [ca. 350 AD]).
20) St. Hilary of Poitiers said that Peter was “the foundation of the Church” and wrote: “And you [Pope Julius], most dearly loved brother, though absent from us in body, were present in mind concordant, and will . . . For this will be seen to be best, and by far the most befitting thing, if to the head, that is to the see of the Apostle Peter, the priests of the Lord report from every one of the provinces” (Fragment 2 ex opere Historico [ex Epistle Sardic. Concil. Ad Julium [before 367 AD]).
21) St. Optatus observed that in “Rome the episcopal chair was given first to Peter” and explained that the true Church must always possess the chair of Peter and orthodox doctrine, which clearly entails that Rome could never abandon the orthodox faith (The Schism of the Donatists [367 AD]).
22) St. Epiphanius endorsed the Roman primacy (Medicine Chest Against All Heresies [375 AD]).
23) St. Basil the Great: “Nearly all the East is being agitated, right honorable father [Pope Damasus], by a terrible storm and tempest. The old heresy, sown by Arius the enemy of truth, has now boldly and unblushingly reappeared . . . I have looked upon the visit of your mercifulness as the only possible solution to our difficulties . . . I have been constrained to beseech you by letter and to be moved to help us . . . In this I am by no means making any novel request, but am only asking what has been customary in the case of men who, before our own day, were blessed and dear to God, and conspicuously in your own case” (Letter 70 [ca. 379 AD]).
24) St. Gregory Nazianzen wrote that Peter was the “rock” in Matthew 16:18 (Oration 26 [ca. 379 AD]).
25) St. Gregory of Nyssa wrote that Jesus built the Church on Peter (Oration on St. Stephen [ca. 395 AD]).
26) St. Jerome: “I follow no leader but Christ and join in communion with none but Your Blessedness, that is, with the chair of Peter. I know that this is the rock on which the Church has been built. Whoever eats the Lamb outside this house is profane. Anyone who is not in the ark of Noah will perish when the flood prevails . . . Since the East, shattered as it is by the long-standing feuds, subsisting between its peoples, is bit by bit tearing into shreds the seamless vest of the Lord . . . I think it my duty to consult the chair of Peter, and to turn to [Rome]” (Letter to Pope Damasus [379 AD]).
27) Pope St. Damasus: “The holy Roman Church has been placed at the forefront not by the conciliar decisions of the other Churches, but has received the primacy by the evangelic voice of our Lord and Savior [in Matthew 16:18-19] . . . The first see, therefore, is that of Peter the Apostle, that of the Roman Church, which has neither stain nor blemish nor anything like it” (The Decree of Damasus [382 AD]).
28) Ambrosiaster: “Whereas the whole world is God’s, yet is the Church said to be His house, of which [Pope] Damasus is at this day the ruler” (Commentary on the Epistle of First Timothy [366-384 AD]).
29) Pope Siricius: “We – or rather, the blessed apostle Peter in us, who, as we trust, protects and keeps us in everything as the heirs of his government – bear the burdens of all these that are burdened” (385 AD).
30) St. John Chrysostom wrote that Christ entrusted His “sheep” (i.e., Christians) “to Peter and his successors” (The Priesthood [ca. 386 AD]).
31) St. Ambrose: “They [the Novatians] have not the succession of Peter, who hold not the chair of Peter, which they rend by wicked schism; and this, too, they do, wickedly denying that sins can be forgiven even in the Church” (Penance [388 AD]).
32) St. Augustine: due to the authority of Rome]; would that the error too might sometime be at an end!” (Sermons [inter 391 – 430 AD]).
33) Pope St. Innocent: “In seeking the things of God, . . . following the examples of ancient tradition, . . . you have strengthened . . . the vigor of your religion with true reason, for you have acknowledged that judgment is to be referred to us, and have shown that you know what is owed to the Apostolic See, if all of us placed in this position are to desire to follow the Apostle himself from whom the episcopate itself and the total authority of this name have merged . . .They did not regard anything as finished, even though it was the concern of distant and remote provinces, until it had come to the notice of this See, so that what was a just pronouncement might be confirmed by the total authority of this See” (Letter to the Council of Carthage [417 AD]).
34) St. Cyril of Alexandria wrote to Pope Celestine asking him to make a ruling on the orthodoxy of Nestorius, bishop of Constantinople: “God requires us to be vigilant in these matters and the ancient customs of the Churches persuades that we should communicate with your Holiness [in Rome]. We do not openly and publicly break off communion with [Nestorius] before communicating these things to your Piety. Deign therefore to declare what seems to you right; and whether one must remain still in communion with him, or ought it to be proclaimed publicly that no one communicated with one who professes to teach such errors?” (Letter to Pope Celestine [ca. 431 AD]).
35) In response, Pope Celestine urged Cyril to act with Rome’s authority in condemning Nestorius “assuring to yourself the authority of our See [Rome] and using our stead and place, you will execute this sentence with the utmost severity” (Letter [ca. 431 AD]).
36) Nestorius, deposed at the Council of Ephesus, later wrote bitterly: “Who was judge? Cyril. Who was accuser? Cyril. Who was Bishop of Rome? Cyril. Cyril was everything.” In his eyes, Cyril had arrogated to himself the authority and prerogatives of the Pope himself.
37) Council of Ephesus (431 AD): The legate of Pope Celestine came to “ratify [the Council’s] determination” in the name of the Pope, stating “There is no doubt, and in fact it has been known in all ages, that the holy and most blessed Peter, prince and head of the apostles, pillar of the faith, and foundation of the Catholic Church, received the keys of the kingdom from our Lord Jesus Christ, the Savior and Redeemer of the human race, and that to him was given the power of loosing and binding sins: who down even to today and forever both lives and judges in his successors. The holy and most blessed pope Celestine, according to due order, is his successor and holds his place, and us he sent to supply his place in this holy synod.” (Acts of Council, Session 3).
38) St. Peter Chrysologus: “We exhort you in every respect, humble brother, to heed obediently what has been written by the Most Blessed Pope of the City of Rome; for Blessed Peter, who lives and presides in his own see, provides the truth of faith to those who seek it. For we, by reason of our pursuit of peace and faith, cannot try cases on the faith without the consent of the Bishop of the City of Rome” (Letter to Eutyches [a monophysite] [449 AD]).
39) Pope St. Leo the Great: “Although bishops have a common dignity, they are not all of the same rank. Even among the most blessed Apostles, though they were alike in honor, there was a certain distinction of power. All were equal in being chosen, but it was given to one to be preeminent over the others. From this formality there arose also a distinction among bishops, and by a great arrangement it was provided that no one should arrogate everything to himself, but in individual provinces there should be individual bishops whose opinions among their brothers should be first; and again, certain others, established in larger cities, were to accept a greater responsibility. Through them the care of the universal Church would converge in the one See of Peter, and nothing should ever be at odds with this head” (Letter of Pope Leo I to Anastasius, Bishop of Thessalonica [ca. 446 AD]).
40) Council of Chalcedon (451 AD): “After the reading of the foregoing epistle [The Tome of Pope Leo], the most reverend bishops cried out: ‘This is the faith of the fathers! This is the faith of the apostles! So we all believe! Thus the orthodox believe! Anathema to him who does not thus believe! Peter has spoken thus through Leo! . . . This is the true faith! Those of us who are orthodox thus believe! This is the faith of the Fathers! . . . Wherefore the most holy and blessed Leo, archbishop of the great and elder Rome, through us, and through this present and most holy synod, together with the thrice blessed and all-glorious Peter the apostle, who is the rock and foundation of the Catholic Church, and the foundation of the orthodox faith, has stripped him [Dioscorus, the bishop of Alexandria following Cyril’s death] of the episcopate” (Acts of the Council, Sessions 2 and 3).
41) Theodoret: “This most holy See [Rome] has preserved the supremacy over all Churches on the earth, for one especial reason among many others; to wit, that it has remained intact from the defilement of heresy. No one has ever sat on that Chair, who has taught heretical doctrine; rather that See has ever preserved unstained the Apostolic grace” (Epistle 116 to Renatus [before 466 AD]).
42) Pope St. Gregory the Great: “Your most sweet holiness, [Eulogius, bishop of Alexandria], has spoken much in your letter to me about the chair of Saint Peter, prince of the apostles, saying that he himself now sits on it in the persons of his successors. And indeed I acknowledge myself to be unworthy . . . I gladly accepted all that has been said, in that he has spoken to me about Peter’s chair, who occupies Peter’s chair. And, though special honor to myself in no wise delights me . . . who can be ignorant that holy Church has been made firm in the solidity of the prince of the apostles” (Letter to Eulogius [597 AD]).
The original context was a thread on how both the Vatican and the Evangelicals have fallen off the boat. It has a number of googy statements, like we can't hold an Ecumenical Council so we admit the Vatican is supreme, blah blah blah (tell that to the meeting on Cyprus) I might address as we go along. If I do, I'll paraphrase (the arguments aren't new) although the poster (who I believe posts here) might recognize his work.