The Revised Standard Version also says “my God”
Rev 3:1 "And to the angel of the church in Sardis write: The words of him who has the seven spirits of God and the seven stars. "I know your works; you have the name of being alive, and you are dead. 3:2 Awake, and strengthen what remains and is on the point of death, for I have not found your works perfect in the sight of my God.
Jesus also used the expression “my God” while He was alive on earth.
John 20:17 Jesus said to her, “Do not hold me, for I have not yet ascended to the Father; but go to my brethren and say to them, I am ascending to my Father and your Father, to my God and your God.”
As to why He would refer to the Father (First Person of the Trinity) as “my God”: one thought is that both times He is making the statement in His incarnate state.
In John, this is obvious as He is physically alive and present in a human body when He speaks.
In the letters to the various Church’s in Revelations, it is made clear when He identifies Himself as one who had “died” (Rev 1:17-19 below). He identifies Himself specifically as united with His risen human body.
1:17 When I saw him, I fell at his feet as though dead. But he laid his right hand upon me, saying, "Fear not, I am the first and the last, 1:18 and the living one; I died, and behold I am alive for evermore, and I have the keys of Death and Hades. 1:19 Now write what you see, what is and what is to take place hereafter.
IMO, it is in the context of His human nature that He speaks of “my God”.