My child's mother moved with my 3 year old son to a different state without telling me.

You would need to file in the state with proper jurisdiction for custody. If they moved less than six months ago then Ohio would still have jurisdiction. You may need to file to establish paternity as well. You state you do not legally pay child support -- if there is a court order and you are not paying according to said order, that may affect your chances of receiving custody. If this is the first hearing regarding custody to establish it, you will need to prove the best interests of the child per statutory factors is to reside with you.