Is it permissible for a child to call his father "Baba"?

There is no legal impediment for a child to call his father "Baba." The default rule is the permissibility of any appellation that does not involve servitude to other than Allah, or excessive glorification and commendation, or ugliness and ill-omen, or imitation of the enemies of Allah. People have become accustomed to this appellation, and scholars have not objected to it.