Legal Question in Family Law in Kentucky

First, owing child support doesn't effect custody rights, but why are you caring for someone else's child, when you are behind in child support for your biological children? From what you've described here, you aren't this baby's father, biologically or legally. You don't have any legal rights over the child now, so you certainly can't give them to anyone else. Your name on the birth certificate is meaningless; when a couple is unmarried there is no presumed father and paternity must be established. Since you aren't the biological father, you're going to have difficulties. If Mom or the biological father (I'm going to assume by "sperm donor" you aren't being literal in the sense that Mom was artificially inseminated using an anonymous donor), assert their rights, or the Cabinet gets involved, you have no standing.

You need to go IMMEDIATELY and seek a consultation with a family law attorney in your jurisdiction to review your options.