Some quotes from early eastern Fathers, or leaders, of the Church and early Councils regarding the Papacy, except for one by the Roman - St. Thomas of Aquinas, who spoke about St. John Chrysostom.
"After the reading of the foregoing epistle, the most reverend bishops cried out: This is the faith of the fathers, this is the faith of the Apostles. So we all believe, thus the orthodox believe. Anathema to him who does not thus believe. Peter has spoken thus through Leo. So taught the Apostles. Piously and truly did Leo teach, so taught Cyril. Everlasting be the memory of Cyril. Leo and Cyril taught the same thing, anathema to him who does not so believe." -Council of Chalcedon, Session II after St. Pope Leo's Tome. The Church believed that the Pope was the successor of St. Peter the Bishop of Rome. The Pope's voice was authoritative, because it conferred to the teachings of the Fathers, the Apostles, and of St. Cyril (previous Ecuмenical Councils).
"The most blessed bishops of Illyria said: Let those who contradict be made manifest. Those who contradict are Nestorians. Those who contradict, let them go to Rome." -Council of Chalcedon, Session V, Those who contradict the Ecuмenical Council's position are to go to Rome, to see Pope Leo.
"And Chrysostom, speaking in the person of Christ, says: “Feed my sheep (John 21:17), that is, in my place be in charge of your brethren.” " St. Thomas of Aquinas, Contra Errores Graecorum, referencing St. John Chrysostom in his homilly 58 on John
St. Ephraem the Syrian, from the 4th century:
“Blessed are you Simon Kepha
Who holds the keys which the Spirit forges
Great is the word and ineffable
...That could stand bind and loose above and below
Blessed are thou who wert as the head
And as the tounge of the body of brotheren
Through Simon was heard the Revelation from the Father
Through the Rock unshakable”
(De Virginitate15.6,7)
Emperor Justinian of Constantinople (520-533)
Writing to the Pope:
Yielding honor to the Apostolic See and to Your Holiness, and honoring your Holiness, as one ought to honor a father, we have hastened to subject all the priests of the whole... Eastern district, and to unite them to the See of your Holiness, for we do not allow of any point, however manifest and indisputable it be, which relates to the state of the Churches, not being brought to the cognizance of your Holiness, since you are the Head of all the holy Churches. (Justinian Epist. ad. Pap. Joan. ii. Cod. Justin. lib. I. tit. 1).
Emperor Justinian of Constantinople (520-533)
"Let your Apostleship show that you have worthily succeeded to the Apostle Peter, since the Lord will work through you, as Surpreme Pastor, the salvation of all." (Coll. Avell. E...p. 196, July 9th, 520, Justinian to Pope Hormisdas).
St. Maximus the Confessor (c. 650)
"The extremities of the earth, and everyone in every part of it who purely and rightly confess the Lord, look directly towards the Most Holy Roman Church and her confession and faith, as t...o a sun of unfailing light awaiting from her the brilliant radiance of the sacred dogmas of our Fathers, according to that which the inspired and holy Councils have stainlessly and piously decreed. For, from the descent of the Incarnate Word amongst us, all the churches in every part of the world have held the greatest Church alone to be their base and foundation, seeing that, according to the promise of Christ Our Savior, the gates of hell will never prevail against her, that she has the keys of the orthodox confession and right faith in Him, that she opens the true and exclusive religion to such men as approach with piety, and she shuts up and locks every heretical mouth which speaks against the Most High." (Maximus, Opuscula theologica et polemica, Migne, Patr. Graec. vol. 90)
St. Maximus the Confessor:
How much more in the case of the clergy and Church of the Romans, which from old until now presides over all the churches which are under the sun? Having surely received this canonically, as well a...s from councils and the apostles, as from the princes of the latter (Peter and Paul), and being numbered in their company, she is subject to no writings or issues in synodical docuмents, on account of the eminence of her pontificate .....even as in all these things all are equally subject to her (the Church of Rome) according to sacerodotal law. And so when, without fear, but with all holy and becoming confidence, those ministers (the popes) are of the truly firm and immovable rock, that is of the most great and Apostolic Church of Rome. (Maximus, in J.B. Mansi, ed. Amplissima Collectio Conciliorum, vol. 10)
St. Theodore the Studite of Constantinople (759-826)
Writing to Pope Paschal:
Hear, O Apostolic Head, divinely-appointed Shepherd of Christ's sheep, keybearer of the Kingdom of Heaven, Rock of the Faith upon whom the Catholi...c Church is built. For Peter art thou, who adornest and governest the Chair of Peter. Hither, then, from the West, imitator of Christ, arise and repel not for ever (Ps. xliii. 23). To thee spake Christ our Lord: 'And thou being one day converted, shalt strengthen thy brethren.' Behold the hour and the place. Help us, thou that art set by God for this. Stretch forth thy hand so far as thou canst. Thou hast strength with God, through being the first of all. (Letter of St. Theodore and four other Abbots to Pope Paschal, Bk. ii Ep. 12, Patr. Graec. 99, 1152-3)