Quoting ☆Tiffanyyy☆:" And if he tries to see him what. Would he have to get the courts involved if I don't let him or have any contact with hm?"
"In Ohio, an unmarried mother is considered to have sole physical and legal custody
of the child, unless an Ohio family court determines someone else to be the legal or physical guardian"
You have sole physical and legal custody unless he requests otherwise, but is he really going to be able to afford thousands of dollars in lawyer and court fees to do so?