When Aslan says "Son of Adam" and "Daughter of Eve," this refers to humans being ACTUALLY DESCENDED FROM Adam and Eve. This reference, furthermore, is one of the ways in which Mister Lewis made it clear that he WAS NOT making up some OTHER omnipotent God. Remember that in "Magician's Nephew," Aslan showed the ability to create SOMETHING FROM NOTHING. Only the actual God has, or ever could have, that power. Thus, Mister Lewis asserted simultaneously that Aslan IS Jesus, and that JESUS is Almighty God.
Like every Christian, Lewis believed that no God exists anyplace or anytime, EXCEPT the God of the Bible; and that this God exists in the Three Persons of the Father, the Son and the Holy Spirit. Lewis would never have knowingly misled his readers into believing that there could be ADDITIONAL Gods if you could just look in other dimensions. Thus, Aslan IS NOT merely "someone who slightly resembles a hint of an allegory of a parable of a likeness of a suggestion of a character vaguely like Jesus." Aslan IS JESUS, the same Jesus Who lived in our history, merely assuming a different external form. If this were not so, Lewis would not have had Aslan say in "Dawn Treader" that He was also present in our world.
To say that Aslan is omnipotent, AND can be found in our world, but is NOT the God of the Bible, WOULD be to say that someone else in our world is ALSO omnipotent God BESIDES the God of the Bible. No Christian would ever give people even a slight encouragement to believe that!
Thus, if you pay attention to what LEWIS HIMSELF said, Aslan is Jesus Christ, peer-ee-od. And since He is Jesus, when He addresses characters as "My son" or "My daughter," this refers to the relationship that is created by the new birth in Jesus.