Does my ex have parental rights if he has no relationship with the child and has never contributed to his care or support?

I have an abusive ex with whom I share a child. He has been in jail for violence against me, during which time I moved. He has not had any kind of involvement with my son for at least a year, and has never contributed in any way to his support or care. I know him to be unstable, with severe behavioral and emotional problems, substance abuse issues and a tendency to violence, with a consistent pattern of criminal activity for most of his adult years. Not the kind of person I would trust with a child. He has been stalking me through social media and through third parties and recently harassed me at my church, all of which causes me great anxiety. I just want him to leave us alone. I fear that pursuing a restraining order will give rise to court ordered time sharing of my son. With his name on the birth certificate, but without any relationship or support established with the child, can his rights be terminated without his involvement in a court hearing? What should I do? What is the best thing for me to do in this case? I want him out of our lives permanently, as I believe him to be dangerous to our emotional health and safety.