However, there were rare instances in which non-Romans objected to Rome’s authority in the first millennium. For the sake of Catholics not being blind-sided in debates, I have listed the big ones:
Pope Victor I and the Quartodeciman Controversy
Pope Victor I threatened to excommunicate the churches of Asia for the practice of Quartodecimanism. Eusebius of Caesarea describes the backlash:
But this did not please all the bishops. And they besought him to consider the things of peace, and of neighborly unity and love. Words of theirs are extant, sharply rebuking Victor.
Pope Stephen I vs Firmilian
Pope Saint Stephen I ordered bishop Saint Cyprian of Carthage and bishop Firmilian of Caesarea not to rebaptize heretic converts. Firmilian wrote an angry letter to Cyprian against Pope Stephen:
But that they who are at Rome do not observe those things in all cases which are handed down from the beginning, and vainly pretend the authority of the apostles.
And in this respect I am justly indignant at this so open and manifest folly of Stephen, that he who so boasts of the place of his episcopate, and contends that he holds the succession from Peter, on whom the foundations of the Church were laid, should introduce many other rocks and establish new buildings of many churches; maintaining that there is baptism in them by his authority.
Stephen, who announces that he holds by succession the throne of Peter, is stirred with no zeal against heretics.The Meletian Party at Antioch
Rome recognized Paulinus, rather than Meletius, as bishop of Antioch in the 4th Century. The Cappadocian Fathers generally supported Meletius. Saint Basil the Great wrote:
I hear, moreover, that the Paulinians are carrying about a letter of the Westerns, assigning to them the episcopate of the Church in Antioch, but speaking under a false impression of Meletius, the admirable bishop of the true Church of God.... Therefore I congratulate those who have received the letter from Rome. And, although it is a grand testimony in their favour, I only hope it is true and confirmed by facts. But I shall never be able to persuade myself on these grounds to ignore Meletius, or to forget the Church which is under him, or to treat as small, and of little importance to the true religion, the questions which originated the division. I shall never consent to give in, merely because somebody is very much elated at receiving a letter from men. Even if it had come down from heaven itself, but he does not agree with the sound doctrine of the faith, I cannot look upon him as in communion with the saints.
Even our beloved Saint Augustine appears to have had less than an absolute view of the Pope’s supremacy. He is likely one of the authors of the Optaremus, in which the North African bishops rather brazenly challenged Pope Celestine I’s authority over Africa:
the Nicene Decrees have most plainly committed not only the clergy of inferior rank but the bishops themselves to their own metropolitans. For they have ordained with great wisdom and justice that all matters should be terminated where they arise ; and they did not think that the grace of the Holy Spirit would be wanting to any province for the priests of Christ [i.e. the bishops] wisely to discern and firmly to maintain that which is right, especially since whosoever thinks himself wronged by any judgement may appeal to the Council of his province or even to a general Council [sc. of all Africa], unless it be imagined that God can inspire a single individual with justice and refuse it to an innumerable multitude of priests [i.e. bishops] assembled in Council.
For that your Holiness should send any on your part, we can find ordained by no Council of the Fathers.
Rome and Alexandria were almost perfectly aligned in every matter for the first 400 years of the Church, but for some reason that fell apart when Dioscorus became Pope of Alexandria. Dioscorus attempted to excommunicate Pope Leo I following the Robber Synod of 449. Dioscorus was in turn excommunicated by the Council of Chalcedon in 451.
All the stirring resentment against Rome in the east came to the fore with Patriarch Photius of Constantinople in the 9th Century, who is perhaps second only to Dioscorus in the 1st millennium for his opposition to the Apostolic See.