When the disciples of Christ asked Jesus how to pray He instructed them to address God as “Our Father.” When Jesus prayed, He also called God “Father.” Yet on the cross, Jesus cries out to God addressing Him as “My God, My God.” This is the only time in Scripture that Jesus directly addresses His Father as “My God.”
This special terminology seems to indicate that something profound was happening within the relationship between God the Father and God the Son. Perhaps it was that at the moment Christ was becoming sin on our behalf He related to God not as His special Father, but as a just and powerful “God.”At the cross "My Father" became "My God."
God told Israel that He would be “their God.” He rewarded their righteousness and punished their wickedness. He was a source of provision and judgment. Many know God is “their God.” He gives them daily provision, but someday will exact justice and respond to sin with appropriate condemnation. But through salvation I do not address God as just "my God" Because of the cross "my God" became "my Father."