The reality is that no one has been able to refute the fact that St Peter is the Rock on which Christ built His Church, and the fact that St Peter was given FIVE mandates as Christ’s chosen Chief Vicar which were given to no one else.
This is confirmed further by more Fathers of the Church.
Optatus
“You cannot deny that you are aware that in the city of Rome the episcopal chair was given first to Peter; the chair in which Peter sat, the same who was head—that is why he is also called Cephas ‘Rock’]—of all the apostles; the one chair in which unity is maintained by all” (*The Schism of the Donatists *2:2 [A.D. 367]).
**Epiphanius of Salamis **
“At Rome the first apostles and bishops were Peter and Paul, then Linus, then Cletus, then Clement, the contemporary of Peter and Paul” (*Medicine Chest Against All Heresies *27:6 [A.D. 375]).
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St. Jerome **
“[Pope] Stephen . . . was the blessed Peter’s twenty-second successor in the See of Rome” (*Against the Luciferians *23 [A.D. 383]).
“Clement, of whom the apostle Paul writing to the Philippians says ‘With Clement and others of my fellow-workers whose names are written in the book of life,’ the fourth bishop of Rome after Peter, if indeed the second was Linus and the third Anacletus, although most of the Latins think that Clement was second after the apostle” (*Lives of Illustrious Men *15 [A.D. 396]).
“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 a church [Rome] whose faith has been praised by Paul [Rom. 1:8]. I appeal for spiritual food to the church whence I have received the garb of Christ. . . . Evil children have squandered their patrimony; you alone keep your heritage intact” (*Letters *15:1 [A.D. 396]).
…“I follow no leader but Christ and join in communion with none but your blessedness [Pope Damasus I], 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” (ibid., 15:2).
“The church here is split into three parts, each eager to seize me for its own. . . . Meanwhile I keep crying, ‘He that is joined to the chair of Peter is accepted by me!’ . . . Therefore, I implore your blessedness [Pope Damasus I] . . . tell me by letter with whom it is that I should communicate in Syria” (ibid., 16:2).
**Peter Chrysologus **
“We exhort you in every respect, honorable 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 Rome” (*Letters *25:2 [A.D. 449]).
americancatholictruthsociety.com/docs/ecfpapacy.htm