If I relinquish my rights would I still be ordered to pay child support?

My son is 14. I have full custody of him from the state of CA which I obtained when I divorced his father. His father came back to my son’s life when he was 3. Soon after my son became very difficult to handle so when my son was 4 he went to live with his dad which at the time lived about 1/2 mile from me. Anyway his father ended up leaving to Ohio which at the time we lived in TX. He's basically kept my son from me and has only allowed my boy to come see me a handful of times. I've always paid for expenses and helped out whenever I could I haven't worked since I remarries because me and my husband decided I would be a stay at home mom to my two older children and out new baby girl. My ex still alienates my son from me and due to the fact that my son suffers from Asperger’s he is still very difficult to deal with especially because he hasn't ever bonded with me, my husband and his sisters. A year ago my son because really abusive on the phone and called me horrible names as his father instigated. I hung up and decided to stop calling him and try to work things out with him once he turns 18 away from his father who holds ill feelings towards me because I left him due to alcoholism, and he had gotten himself kicked out of the Army for drugs. Anyway now he's asking for child support. I don't work and no one in our home benefits from any sort of relationship with him. My son was suspended for making terroristic threats and actually hit me during his last visit. He speaks so hatefully about me and things he says he's heard from his father. I was thinking of just relinquishing rights as a parent to my son, yes it hurts but this is what they want anyway is fore to be gone. I'm actually afraid for my life. What can I do? If I relinquish my rights would I still be ordered to pay child support? I now reside in Madison Alaba and they live in Akron Ohio.