Theophylact of Ohrid

And set up over His head His accusation written, THIS IS JESUS KING OF THE JEWS. That which the evangelist John calls His "title" (Jn. 19.19), Matthew calls His "accusation." For they wrote down an indictment giving the reason for His crucifixion, namely, that He was accused of claiming to be "King of the Jews" and of leading an insurrection. They indicted Him as "King" meaning to slander Him, but in truth their indictment was unimpeachable evidence admitted by his adversaries. …

Commentary on Matthew ↗

Jerome

And they placed over his head the charge against him, written, 'This is Jesus, the King of the Jews.' I cannot sufficiently admire the magnitude of the matter, that, for the sake of the redeemed, with a false accusation and having incited the unfortunate people to sedition and outcry, they found no other cause for his execution except that he was the King of the Jews. And perhaps they did this in mockery and ridicule. …

Commentary on Matthew ↗

Thomas Aquinas

Then the title follows: "and they put over his head his cause written etc." And it should be noted that what they did for his disgrace, by God's ordinance, turned to his honor. Hence they put his cause, i.e., the cause for which he suffered; Apocalypse 19:16 has written: "King of kings, and Lord of lords." Therefore, that it says "King of the Jews" pertains to his honor, because he was to be king over all nations; Psalm 2:6: "but I am appointed king by him over Sion, his holy mountain."

Commentary on Matthew ↗

Rabanus Maurus

For because He is at once King and Priest, when He would offer the sacrifice of His flesh on the altar of the cross, His title set forth His regal dignity. And it is set over and not beneath the cross, because though He suffered for us on the cross with the weakness of man, the majesty of the King was conspicuous above the cross; and this He did not lose, but rather confirmed, by the cross.

Catena Aurea by Aquinas ↗