This is a more concise version of my list of quotes from Eastern Fathers supporting the Papacy. I'd suggest using this version, as it's more to the point and relatively short, and thus it's more likely that the quotes will actually be read. These quotes seem to have been taken from the book Jesus, Peter & the Keys by Scott Butler, Norman Dahlgren and David Hess. Thanks to Deacon David Hess for permission to use these quotes on my site.

St. John Cassian, Monk:

That great man, the disciple of disciples, that master among masters, who wielding the government of the Roman Church possessed the principle authority in faith and in priesthood. Tell us, therefore, we beg of you, Peter, prince of Apostles, tell us how the Churches must believe in God (Cassian, Contra Nestorium, III, 12, CSEL, vol. 17, p. 276).

St. Sophronius, Patriarch of Jerusalem:

Transverse quickly all the world from one end to the other until you come to the Apostolic See (Rome), where are the foundations of the orthodox doctrine. Make clearly known to the most holy personages of that throne the questions agitated among us. Cease not to pray and to beg them until their apostolic and Divine wisdom shall have pronounced the victorious judgement and destroyed from the foundation ...the new heresy. (Sophronius,[quoted by Bishop Stephen of Dora to Pope Martin I at the Lateran Council], Mansi, x., 893)

Stephen, Bishop of Dora in Palestine:

[addressed to Pope Martin I]
And for this cause, sometimes we ask for water to our head and to our eyes a fountain of tears, sometimes the wings of a dove, according to holy David, that we might fly away and announce these things to the Chair [the Chair of Peter at Rome] which rules and presides over all, I mean to yours, the head and highest, for the healing of the whole wound. For this it has been accustomed to do from old and from the beginning with power by its canonical or apostolic authority, because the truly great Peter, head of the Apostles, was clearly thought worthy not only to be trusted with the keys of heaven, alone apart from the rest, to open it worthily to believers, or to close it justly to those who disbelieve the Gospel of grace, but because he was also commissioned to feed the sheep of the whole Catholic Church; for 'Peter,' saith He, 'lovest thou Me? Feed My sheep.' And again, because he had in a manner peculiar and special, a faith in the Lord stronger than all and unchangeable, to be converted and to confirm his fellows and spiritual brethren when tossed about, as having been adorned by God Himself incarnate for us with power and sacerdotal authority .....And Sophronius of blessed memory, who was Patriarch of the holy city of Christ our God, and under whom I was bishop, conferring not with flesh and blood, but caring only for the things of Christ with respect to your Holiness, hastened to send my nothingness without delay about this matter alone to this Apostolic see, where are the foundations of holy doctrine. (Mansi, x., 893)

Sergius, Metropolitain of Cyprus:

[ Writing to Pope Theodore ]
O Holy Head, Christ our God hath destined thy Apostolic See to be an immovable foundation and a pillar of the Faith. For thou art, as the Divine Word truly saith, Peter, and on thee as a foundation-stone have the pillars of the Church been fixed. (Sergius Ep. ad Theod. lecta in Sess. ii. Concil. Lat. anno 649)

St. Maximos the Confessor:

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 to 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)

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? ... 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)

If the Roman See recognizes Pyrrhus to be not only a reprobate but a heretic, it is certainly plain that everyone who anathematizes those who have rejected Pyrrhus also anathematizes the See of Rome, that is, he anathematizes the Catholic Church. I need hardly add that he excommunicates himself also, if indeed he is in communion with the Roman See and the Catholic Church of God ...Let him hasten before all things to satisfy the Roman See, for if it is satisfied, all will agree in calling him pious and orthodox. For he only speaks in vain who thinks he ought to persuade or entrap persons like myself, and does not satisfy and implore the blessed Pope of the most holy Catholic Church of the Romans, that is, the Apostolic See, which is from the incarnate of the Son of God Himself, and also all the holy synods, according to the holy canons and definitions has received universal and supreme dominion, authority, and power of binding and loosing over all the holy churches of God throughout the whole world. (Maximus, Letter to Peter, in Mansi x, 692).

John VI, Patriarch of Constantinople:

The Pope of Rome, the head of the Christian priesthood, whom in Peter, the Lord commanded to confirm his brethren. (John VI, Epist. ad Constantin. Pap. ad. Combefis, Auctuar. Bibl. P.P. Graec.tom. ii. p. 211, seq.)

St. Nicephorus, Patriarch of Constantinople:

Without whom [the Romans presiding in the seventh Council] a doctrine brought forward in the Church could not, even though confirmed by canonical decrees and by ecclesiastical usage, ever obtain full approval or currency. For it is they [the Popes of Rome] who have had assigned to them the rule in sacred things, and who have received into their hands the dignity of headship among the Apostles. (Nicephorus, Niceph. Cpl. pro. s. imag. c 25 [Mai N. Bibl. pp. ii. 30]).

St. Theodore the Studite of Constantinople:

[ Writing to Pope Leo III ]
Since to great Peter Christ our Lord gave the office of Chief Shepherd after entrusting him with the keys of the Kingdom of Heaven, to Peter or his successor must of necessity every novelty in the Catholic Church be referred. [Therefore], save us, oh most divine Head of Heads, Chief Shepherd of the Church of Heaven. (Theodore, Bk. I. Ep. 23)

[ 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 Catholic 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. 43:23/44:23). 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)

[ Writing to Emperor Michael ]
Order that the declaration from old Rome be received, as was the custom by Tradition of our Fathers from of old and from the beginning. For this, O Emperor, is the highest of the Churches of God, in which first Peter held the Chair, to whom the Lord said: Thou art Peter ...and the gates of hell shall not prevail against it. (Theodore, Bk. II. Ep. 86)

I witness now before God and men, they have torn themselves away from the Body of Christ, from the Supreme See [Rome], in which Christ placed the keys of the Faith, against which the gates of hell (I mean the mouth of heretics) have not prevailed, and never will until the Consummation, according to the promise of Him Who cannot lie. Let the blessed and Apostolic Paschal [Pope St. Paschal I] rejoice therefore, for he has fulfilled the work of Peter. (Theodore Bk. II. Ep. 63).

In truth we have seen that a manifest successor of the prince of the Apostles presides over the Roman Church. We truly believe that Christ has not deserted the Church here [Constantinople], for assistance from you has been our one and only aid from of old and from the beginning by the providence of God in the critical times. You are, indeed the untroubled and pure fount of orthodoxy from the beginning, you the calm harbor of the whole Church, far removed from the waves of heresy, you the God-chosen city of refuge. (Letter of St. Theodor & Four Abbots to Pope Paschal).