Abba means father, not God. Yet Abba is never used in any context other than God the Father. If abba was referring to the biological father of Barabbas such a designation would be poinless because every man has a biological father. This would be as pointless as to call someone "the one who breathes air."  

Mark 14:36:
And he said, Abba, Father, all things are possible unto thee; take away this cup from me: nevertheless, not what I will, but what thou wilt

Romans 8:15:
For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father.

Galatians 4:6:
And because ye are sons, God hath sent forth the Spirit of his Son into your hearts, crying, Abba, Father.

Barrabas by his name claims to be the son of God, yet Jesus does not make this claim. If Jesus was God, then he wd have been praying to himself in Mark 14:36. If Abba meant the parental father, then Jesus wd have been praying to Joseph, the husband of Mary.