Yup, technically he has no legal rights if he is not on the BC. He will have to go through the process with the court to file to be added to the BC, which generally involves a paternity test if either party requests it. Only then could he petition for visitation/custody. Do you think he will really go through that process or is he just trying to get to you? Does he see your son now? What is the issue that prompted you to want to terminate his rights/him to file for custody?
FWIW, no, you cannot just terminate his rights-in many states, you would need another parent ready to adopt even if he was willing to terminate, but from my understanding, he would have to abandon your child for a certain period of time to involuntarily terminate (meaning no contact, no child support, etc.)
Single mama to dd and ds , loving my dsd always .