I live in ohio and i need to know child custody laws?

I live in ohio I wa married and then i got a divorce and soon i found out i concived when i was married does that mean that my ex husband has custody of the baby since we were married when i concived? Is been to my understanding if you have a child out of wedlock the mother is the only one that has custody. Also I was wondering if his mother can try to fight for custody? She let me move in with her because when me n her son got a divorce i threaten to get alimony from him. So can she use the fact that im stayin in her house and I dont have my own place against me and will she be able to obtain custody because of my situation?