Augustine of Hippo

As for the right hand of the Father, it isn't meant in the manner of the structure of the human body, as though he is on the Son's left, if the Son in terms of bodily positions and relationships is placed on his right. But the right hand of God means the inexpressible peak of honor and good fortune, as we read it said about wisdom: "His left hand under my head, and his right hand embraces me." If earthly convenience has been lying underneath, then eternal felicity is embracing from above.

Sermon 214:8 ↗

Gregory the Dialogist

But we must note what it means that the angel is seen sitting on the right side. For what is designated by the left except the present life, and what by the right except eternal life? Hence it is written in the Song of Songs: "His left hand is under my head, and his right hand shall embrace me." Since therefore our Redeemer had already passed beyond the corruption of the present life, rightly the angel who had come to announce his eternal life was sitting on the right.

Forty Gospel Homilies, Homily 21 ↗

Bede

His left hand under my head, etc. In the left hand of Christ, temporal gifts are signified, and in the right hand, the happiness of eternal life. Therefore it is written elsewhere of him, who is the power and wisdom of God, "Length of days is in his right hand, and in his left hand riches and glory." Therefore the holy Church shows, the soul perfectly intent on the love of its Redeemer shows, what kind of rest it might find in this life which it so eagerly seeks, how it desires to lie in that flowery bed of virtues with its beloved …

Commentary on the Song of Songs ↗