Abba is as far as I can find the only Aramaic word for father.
Easton's Bible Dictionary - AbbaBecause JESUS says, "Abba, Father," in these three places in scripture, it leads me to believe that there are two different Aramaic expressions for father, and the original Greek manuscript of the scriptures made the distinction by using the Aramaic for Jesus' affectionate name for his father, followed by the formal Aramaic word for Father, whatever it is, translated into Greek.
This Syriac or Chaldee word is found three times in the New Testament (Mark 14:36; Romans 8:15; Galatians 4:6), and in each case is followed by its Greek equivalent, which is translated "father." It is a term expressing warm affection and filial confidence. It has no perfect equivalent in our language. It has passed into European languages as an ecclesiastical term, "abbot."
I've always been told that "Abba" is an affectionate name, like Daddy or Papa. But the word Father can be both a name for a person, the name of a biological reality, or the name of a relationship status. It would be like our saying, "Daddy, Father."
The feminists can whine all they want, but there is a reason God directed the scriptures to reflect maleness for God and Jesus, even though God most probably does not have a male or female sex such as the way fleshly humans do. God wants males and femaels to relate to one another in certain ways, and not in others. That's why he gave specific instructions not to dress in the clothing of the opposite sex or engage in same-sex relations.