Eastern Fathers
Desert Fathers
Daniel told a story of another hermit who used to live in the lower parts of Egypt, and who said in his simplicity that Melchizedek was the Son of God. Now when the blessed man Theophilus, the archbishop of Alexandria, heard of it, he sent a message asking the monks to bring the hermit to him. When he saw him, he realized that he was a man of vision and that every thing that he had asked for God had given him, and that he had only said this out of simplicity. …
The Desert Fathers, Sayings of the Early Christian Monks ↗
Cosmas Indicopleustes
Then immediately again with reference to his humanity he says: The Lord hath sworn and will not repent, Thou art a priest for ever after the order of Melchisedec; for deity does not exercise the priestly office or render worship, but is rather itself worshipped and the recipient of sacred services.
The Christian Topography, Book 5 ↗
Western Saints
Augustine of Hippo
And unto what are You born? "The Lord has sworn, and will not repent: You are a Priest for ever after the order of Melchizedec" [Psalm 110:4]. For unto this were You born from the womb before the morning star, that You might be a Priest for ever after the order of Melchizedec. For in that character in which He was born of the Father, God with God, coeternal with Him who begot Him, He is not a Priest; but He is a Priest on account of the flesh which He assumed, on account of the victim which He was to offer for us received from us. …
Exposition on Psalm 110 ↗
Jerome
The Lord has sworn, and he will not repent. "The Lord has sworn." In what he says, "he has sworn," it is not to the one who was begotten before the morning star, but he swore to the one who after the morning star was born of the Virgin. You are a priest forever according to the order of Melchizedech. It is superfluous for us to wish to interpret this little verse, since the holy Apostle argued about it most fully to the Hebrews. For this Melchizedech himself is without father, without mother, without lineage. …
Homily 36, on Psalm 109 ↗