Do you have any idea from what village your Babyak/Babjak ancestors came? Knowing the village of your ancestors is one of the most important things to getting help from others in your research.
Besides mine (from a village between Svidnik & Bardejov, Saros county, Slovakia), I know there's a Babyak (Babjak also the original spelling of that one) from another area (Either close to or now in what is now western Ukraine).
If I can be of any help, let me know.
MARIANNE