To the OP:
I found some more quotes
“My words are spoken to the successor of the fisherman, to the disciple of the cross. As I follow no leader save Christ, so I communicate with none but your blessedness, that is with the chair of Peter. For this, I know, is the rock on which the church is built! Matthew 16:18 This is the house where alone the paschal lamb can be rightly eaten. Exodus 12:22 This is the ark of Noah, and he who is not found in it shall perish when the flood prevails. Genesis 7:23 … He that gathers not with you scatters; Matthew 12:30 he that is not of Christ is of Antichrist.”
– St Jerome, Letter 15, to Pope Damasus.
from A Guide to the Thought of Saint Augustine by Fr. Eugène Portalié, S.J.
c. ORGANIZATION OF THE HIERARCHY
The essential superiority of the episcopacy over the priesthood was recognized by Augustine. In his work On Heresies he mentions the error of Aerius who had denied this. 56 This passage should clear up a statement in a letter to St. Jerome in which an expression of humility could be misinterpreted. 57
Finally, at the summit of the hierarchy, he proclaimed the primacy of the Bishop of Rome and recognized the monarchical character of government established by Jesus Christ in His Church. Attempts have been made to make Augustine an Episcopalian who would admit the equality of all the bishops and not recognize a sovereign authority either in St. Peter or his successors. 58 The further charge is made that he maintained that the Bishop of Rome is only the representative, the symbol of the unity of the Church, not the principle of a true sovereign authority. 59 Explicit passages, however, and the whole conduct of the Bishop of Hippo 60 give the lie to these assertions.
Augustine affirms the Primacy of Peter among the Apostles with a clarity which dispels all doubt. The comparison between St. Cyprian and St. Peter must be read: In martyrdom they are equal, but what a preeminence of dignity in Peter “in whom the primacy of the Apostles shone forth with such excelling grace. … For who does not know that that primacy over the apostolate is to be preferred to any other bishopric? 62 Peter represented the Church when he received the keys, not in this sense that this power was handed over to the community, as some still claim, 63 but as the head of a people representing this people: “The Apostle Peter, because of the primacy of his apostolate, personified this Church, symbolizing her generality.” 64 pp. 237ff.
“We greatly wondered that in your imperial commands, directed for the Patriarch of the royal city, Tarasius, we find him there called Universal. … Because if he be named Universal, above the holy Roman Church which has a prior rank, which is the head of all the Churches of God, it is certain that he shows himself as a rebel against the holy Councils, and a heretic.”
“For, if he is Universal, he is recognized to have the Primacy even over the Church of our See, which appears ridiculous to all faithful Christians: because in the whole world the chief rank and power was given to the blessed Apostle Peter by the Redeemer of the world himself; and through the same Apostle [not merely for political or geographical reasons], whose place we unworthily hold, the holy Catholic and Apostolic Roman Church holds the first rank, and the authority of power, now and for ever…”
Second Council of Nicæa
“Paschasinus, the most reverend bishop and legate of the Apostolic See, stood up in the midst with his most reverend colleagues and said: We received directions at the hands of the most blessed and apostolic bishop of the Roman city, which is the head of all the churches…”
Council of Chalcedon (A.D. 451)