Augustine of Hippo

Since in Matthew's genealogy is showed forth the taking on Him by Christ of our sins, therefore he descends from David to Solomon, in whose mother David had sinned. Luke ascends to David through Nathan, for through Nathan the prophet God punished David's sin; because Luke's genealogy is to show the putting away of our sins. (Lib. Retract. ii. 16.) That is it, must be said, through a prophet of the same name, for it was not Nathan the son of David who reproved him, but a prophet of the same name.

Catena Aurea by Aquinas ↗

Ambrose of Milan

But the holy David is the more excellent in this, that he confessed himself to be but man, and neglected not to wash out with the tears of repentance the sin of which he had been guilty, in so taking away Urias' wife. Herein showing us that none ought to trust in his own strength, for we have a mighty adversary whom we cannot overcome without God's aid. …

Catena Aurea by Aquinas ↗

Thomas Aquinas

Jesse was the father of David the king. David is taken to mean strong hand and fair to behold; both of which suit Christ, as is evident. For he was strong in overcoming the devil. "But when one stronger than he assails him and overcomes him, he takes away his armor in which he trusted and divides his spoil" (Lk 11:22). Also "he is the fairest of the sons of men" (Ps 45:2). But why was it that, since many of the others were kings, he is called king? …

Commentary on Matthew ↗