Peter and his successors have been supreme in the Church from the moment Jesus Christ ascended into Heaven.
The power of the Popes in the ante-Nicene church:
Pope Clement I asserted the authority of Rome over the Church of Corinth as early as 69-90 AD. newadvent.org/fathers/1010.htm
Patriarch Ignatius I of Antioch referred to Rome alone as the "presiding church." newadvent.org/fathers/0107.htm
Saint Irenaeus of Lyons stated that it was necessary for all churches everywhere to agree with the Church of Rome, since it was founded by the Apostles Peter and Paul. newadvent.org/fathers/0103303.htm
Pope Victor I asserted Rome's authority over the churches of Asia. newadvent.org/fathers/250105.htm
Saint Cyprian of Carthage referred to Rome as the "chief church" and the "throne of Peter", from which sacerdotal unity takes its source. newadvent.org/fathers/050654.htm
Pope Stephen I asserted Rome's authority over the churches of Cappadocia. newadvent.org/fathers/050674.htm
Pope Dionysius I deposed Patriarch Paul of Antioch. newadvent.org/fathers/250107.htm
Saint Irenaeus of Lyon newadvent.org/fathers/0103303.htm
Since, however, it would be very tedious, in such a volume as this, to reckon up the successions of all the Churches, we do put to confusion all those who, in whatever manner, whether by an evil self-pleasing, by vainglory, or by blindness and perverse opinion, assemble in unauthorized meetings; by indicating that tradition derived from the apostles, of the very great, the very ancient, and universally known Church founded and organized at Rome by the two most glorious apostles, Peter and Paul; as also the faith preached to men, which comes down to our time by means of the successions of the bishops. For it is a matter of necessity that every Church should agree with this Church, on account of its preeminent authority, that is, the faithful everywhere, inasmuch as the tradition has been preserved continuously by those who exist everywhere.
Saint Cyprian of Carthage newadvent.org/fathers/050654.htm:
After such things as these, moreover, they still dare— a false bishop having been appointed for them by, heretics— to set sail and to bear letters from schismatic and profane persons to the throne of Peter, and to the chief church whence priestly unity takes its source; and not to consider that these were the Romans whose faith was praised in the preaching of the apostle, to whom faithlessness could have no access.
The Formula of Hormisdas byzcath.org/forums/ubbthreads.php/topics/122063/The%20Formula%20of%20Pope%20St%20Hormisd
For it is impossible that the words of our Lord Jesus Christ, who said, "Thou art Peter, and upon this rock I will build my Church," should not be verified. And their truth has been proved by the course of history, for in the Apostolic See the Catholic religion has always been kept unsullied.
The Sixth Ecumenical Council newadvent.org/fathers/3813.htm)::)
For this is the rule of the true faith, which this spiritual mother of your most tranquil empire, the Apostolic Church of Christ, has both in prosperity and in adversity always held and defended with energy; which, it will be proved, by the grace of Almighty God, has never erred from the path of the apostolic tradition, nor has she been depraved by yielding to heretical innovations, but from the beginning she has received the Christian faith from her founders, the princes of the Apostles of Christ, and remains undefiled unto the end, according to the divine promise of the Lord and Saviour himself, which he uttered in the holy Gospels to the prince of his disciples: saying, Peter, Peter, behold, Satan has desired to have you, that he might sift you as wheat; but I have prayed for you, that (your) faith fail not. And when you are converted, strengthen your brethren. Let your tranquil Clemency therefore consider, since it is the Lord and Saviour of all, whose faith it is, that promised that Peter's faith should not fail and exhorted him to strengthen his brethren, how it is known to all that the Apostolic pontiffs, the predecessors of my littleness, have always confidently done this very thing: of whom also our littleness, since I have received this ministry by divine designation, wishes to be the follower, although unequal to them and the least of all.
The Seventh Ecumenical Council - newadvent.org/fathers/3819.htm
"And especially if you follow the tradition of the orthodox Faith of the Church of the holy Peter and Paul, the chief Apostles, and embrace their Vicar, as the Emperors who reigned before you of old both honoured their Vicar, and loved him with all their heart: and if your sacred majesty honour the most holy Roman Church of the chief Apostles, to whom was given power by God the Word himself to loose and to bind sins in heaven and earth. For they will extend their shield over your power, and all barbarous nations shall be put under your feet: and wherever you go they will make you conquerors. "For the holy and chief Apostles themselves, who set up the Catholic and orthodox Faith, have laid it down as a written law that all who after them are to be successors of their seats, should hold their Faith and remain in it to the end."
Dicatus Papae of Pope Gregory VII en.wikisource.org/wiki/Select_Historical_Documents_of_the_Middle_Ages/Book_IV/The_Dictate_of_the_Pope
"That the Roman church has never erred; nor will it err to all eternity, the Scripture bearing witness."