In the garden of Gethsemane, Jesus is quoted as saying, “…Abba, Father, all things are possible unto thee…” Mark 14:36. ‘Abba’ is Strong’s word G5. Vines Expository Dictionary of New Testament Greek explains the word as following: “…Abba is the word framed by the lips of infants, and betokens unreasoning trust; ‘father’ (or pater) expresses an intelligent apprehension of the relationship. The two together express the love and intelligent confidence of the child…” If this scripture used the exact words (not a Greek translation) of Jesus when he addressed God, then Jesus called God, “Abba, Father”.
On the cross, Jesus cried, “…Eli, Eli, laba sabachthani? that is to say, My God, my God, why hast thou forsaken me?” (Matthew 27:46) These are the first words of Psalm 22 in the Aramaic language (used by the Jews in Jesus’ time). ‘Eli’ has the thought of ‘my God’.
Other words which Jesus used in referring to His Father are not known, because the Gospels were written in Greek and Jesus spoke in Aramaic. Strong's Concordance word #3962, “pater” in Greek, was the word used in John 8:18, 19. "I am the one that bear witness of myself, and the Father (pater) that sent me beareth witness of me….Ye neither know me, nor my Father (pater): if ye had known me, ye should have known my Father (pater) also.”
Jesus may also have used the Hebrew, YHWH, or Yahweh with vowels added, which was considered God’s most sacred name. Rotherham discusses this in great detail and cites Exodus 3:14, 15. "And God said unto Moses, I Will Become whatsoever I please. And he said–Thus shalt thou say to the sons of Israel, I Will Become has sent me unto you. And God said yet further unto Moses–Thus shalt thou say unto the sons of Israel, Yahweh, God of your fathers, God of Abraham, God of Isaac, and God of Jacob hath sent me unto you. This is my name to times age-abiding, and this my memorial to generation after generation."