Historical facts will not play in your favor with regard to Papal Supremacy
According to the fourth-century historian Eusebius, Patriarch Dionysius of Antioch (died ca. 264) wrote to Pope Xystus II asking about rebaptism. He asked for advice from the Pope, he said, “for fear I am acting mistakenly.” Later the Patriarch wrote to Xystus’s successor, Pope Dionysius, informing him that the Sabellian heresy had appeared in his patriarchate. (This trinitarian heresy so emphasized the unity of the Godhead as to deny a distinction of divine Persons.) The Pope also wrote to two of his Egyptian bishops, emphasizing our Lord’s humanity. Certain persons in the see of Alexandria (perhaps those two bishops) reported to the Pope that Patriarch Dionysius was tending toward heretical views.
The Pope wrote the Egyptian bishops a letter detailing the errors of Sabellianism and what was later called Arianism and condemning them. He designated the term homoousios (“of the same substance”) as an appropriate safeguard of orthodox Christology. Note that sixty and more years before the Council of Nicaea, Pope Dionysius anticipated the Council’s work in condemning Arianism and in selecting the appropriate theological concept for the Church’s Christology.
The Pope wrote to Patriarch Dionysius, told him of the allegations against his orthodoxy, and asked for an explanation. Eastern Orthodox apologists tell us the Pope had no jurisdiction over other bishops. Here the Pope is calling on the second most important bishop of the Christian world to defend his orthodoxy. Did Patriarch Dionysius deny the Pope’s authority to bring him on the carpet, so to speak? Not at all. He welcomed the Pope’s inquiry and quickly wrote an explanation which the Pope accepted as satisfactory.
In the third century Paul of Samosata, bishop of Antioch, denied the personhood of the Logos, saying that only the divine Wisdom had become incarnate. In 264 the bishops of Syria, Palestine, and Asia Minor convened in synod and condemned Paul’s heresy. Because he persisted in his errors, a second and then a third synod met, and finally he was deposed and excommunicated. Domnus was named as replacement, but Paul refused to vacate the episcopal residence. The bishops appealed to Emperor Aurelian, who was in Antioch at that time. It would have been simple for the Emperor to settle the matter then and there and order Domnus installed as patriarch of Antioch. Instead, he asked Rome to decide who should be patriarch. Rome chose Domnus, and he was installed.
Note that this was a controversy among Eastern bishops, and it involved the rightful occupant of the third most important see in the Church, an Eastern see. Why did Aurelian turn to Rome for a decision? Why would he have the controversy settled in a way that would be a staggering affront to the Eastern bishops and to their authority . . . unless they recognized the pope’s universal jurisdiction. That they did. None objected. The matter was settled. " Roma locuta est" (Rome has spoken).