Pope Julius (337-352)
The Eusebians believed that since Rome reserved the right to depose Novation without the East the East should have the freedom to depose Athanasius without interference from the West. Julius responded to them in a letter which was preserved by Athanasius:
It behooved you, beloved, to come hither [to Rome], and not to refuse, in order that this business may be terminated, for reason requires this... O beloved!...For even if any offenses had been committed by these men, as you say, the judgment ought to have been in accordance with the rule of the church, and not thus...And why were we not written to especially with regard to the church of Alexandria? Or are you ignorant that this has been the custom, first to write to us, and that thus what is just be decreed from here? If therefore any such suspicion fell upon the bishop there [at Alexandria], it was befitting to write to this church. Not thus were the ordinances of Paul, not thus have the Fathers handed it down to us. This is a new decree, and a new institution. Bear with me, I exhort you, for what I write is for the common good. For what we have received from the blessed apostle Peter, the same do I manifest to you. [Apol., 35. PG 25: 305-8]
Socrates wrote(306-439 aprox.) that Julius rebuked the Eusebians on the grounds that:
...it is unlawful to legislate for the churches without the consent of the bishop of Rome [HE II, 17 ]
Maximus the Confessor (580-662) who said that the Apostolic See of Rome:
... from God the Incarnate Word Himself as well as all the holy Councils, according to the sacred canons and definitions, has received and possesses supreme power in all things and for all things, over all the holy churches of God throughout the world, as well as power and authority of binding and loosing. For with this church, the Word, who commands the powers of heaven, binds and looses in heaven. [PG 91: 144]
Council of Sardica (343)
... most beloved brother, although you were separated in the body, you were present by a like mind and will...For this will seem best and most exceedingly fitting if the bishops of the Lord, from each of the different provinces, refer to the head [caput], that is, the see of Peter the apostle...[Mansi 3: 40]
Pope St. Gregory the Great (590-604)
Pope Gregory proclaims that the Apostolic See is head of all the churches. [Epp. XIII, 45. PL 77, 1298]