As the father of a child in Ohio, you may worry about your legal rights. It used to be that fathers had little rights and the mother usually had all the control, but times have changed. The law now is such that it aims to involve both parents equally in the decision making and raising of a child. This is also true if the child is placed for adoption. According to Adoption from the Heart, you have the exact same rights as the mother when it comes to adoption.
You may be in a situation where you are not aware your child is being put up for adoption. The law has built in safeguards for this situation. It is required that officials try to contact you. If they cannot get directly in contact with you, they must provide a public notice of the adoption. This gives you every chance to step in and object. However, if you do object, you need to prove you have had a relationship with the child or show you have tried to have a relationship with the child prior to the adoption.
In any case, both the mother and father must give up their parental rights for a legal adoption of a child. It is possible for the court to terminate parental rights if the parents are unable to do so. So, even if the court cannot find you and you did not respond to any notices, the court has the ability to terminate your rights.
Do keep in mind, if you were not married to the mother, your rights are only considered if you established paternity. Otherwise, you are not considered the legal father and are unlikely to get notice of any pending adoption. If you were married to the mother, then you should receive prompt notification. This information is for education and is not legal advice.