Will the Father Be the God of Jesus the Messiah Eternally?

Few statements in Scripture can match the profundity of Revelation 3:12:


Him that overcometh will I make a pillar in the temple of my God, and he shall go no more out: and I will write upon him the name of my God, and the name of the city of my God, which is new Jerusalem, which cometh down out of heaven from my God: and I will write upon him my new name.

In this statement by the risen, ascended, and exalted Messiah, Jesus of Nazareth, who was and always will be the God-Man, He emphatically reveals to us that the Father was still His God even after He had been enthroned on high at the right hand of the Father.

The Spirit clearly intends for all believers to profit in our day from this unfathomably profound statement. Does this statement also teach us that the Father will be the God of Jesus the Messiah eternally?