In 2005 i became pregnant with my first son. When i finally got up enough courage to tell the father he had been arrested for arson, controlled substance, and theft. (I had no idea he was into that)When i told R.T., the biological father, he was exstatic about it. He told me that he wanted to be a part of the childs life and i explained that i would be willing to allow him to see our child after he got out but i would have to be there. During this time my best friend, now my husband, told me it was a bad idea. I explained i would give him the benefit of doubt and allow him to see him. after R.T. was released on parole i never heard a word from him. When my son was 2 i had to get a paternity test to keep my medical coverage. R.T. was told he had to pay child support of 0.00 (he was in prison and a judge never set an amount) R.T. is not on the birth certificate, has never paid a cent, has never seen my son, and is in and out of prison. My husband wants to Adopt our son but we dont know where to begin. Does R.T. have any rights at all? How do we relinquish his rights if he does?

In 2005 i became pregnant with my first son. When i finally got up enough courage to tell the father he had been arrested for arson, controlled substance, and theft. (I had no idea he was into that)When i told R.T., the biological father, he was exstatic about it. He told me that he wanted to be a part of the childs life and i explained that i would be willing to allow him to see our child after he got out but i would have to be there. During this time my best friend, now my husband, told me it was a bad idea. I explained i would give him the benefit of doubt and allow him to see him. after R.T. was released on parole i never heard a word from him. When my son was 2 i had to get a paternity test to keep my medical coverage. R.T. was told he had to pay child support of 0.00 (he was in prison and a judge never set an amount) R.T. is not on the birth certificate, has never paid a cent, has never seen my son, and is in and out of prison. My husband wants to Adopt our son but we dont know where to begin. Does R.T. have any rights at all? How do we relinquish his rights if he does?

Apparently, the court established him as the legal father, even though no CS was ordered.
You will need to either get his permission, or go to court to have his rights terminated involuntarily.

You should take all court orders, etc to a local adoption attorney for a consult, then go from there.