Congratulations on your baby.
First thing. Your baby CANNOT be taken from you. (Unless he is at risk of significant harm in your care). No court in this land is going to take a baby from his mum to give to a 16 yr old who has acted as he has.(even if he hadn’t tbh).
Second thing. DO NOT PUT the FATHER on the birth certificate. If you do, he will get legal rights called “Parental Responsibility”. This gives him the right to a say in your child’s upbringing. Given his violent behaviour, you do NOT want this. You do NOT need to put this on the certificate. It is YOUR choice. So DONT.
He can apply to a court for parental responsibility but it’s far from likely he’ll get it based on current and past behaviour.
Thirdly. Confide in your midwife and health visitor. You are very vulnerable at the moment. I would imagine you are scared of the father. As you are so young, the Health visitor should be able to give support and let you know where you can get advice. You do NOT have to let the father see your son, given his threats to take him off you, and given his violence. At some point, there may need to be contact, BUT this has to be in a way that doesn’t put you or your son at risk. At the moment if you do let him see your DS, it should only be when you have your DM or someone who is strong enough to support you with you, and it should be at your house, given his threats.
Fourth. Keep a DIARY of your contact with the father. Log ALL CALLS, and what was said.
You need legal advice, but for now, just think of YOU and your baby. Ignore their threats. Believe me, as long as you care for your DS, they CANNOT take him from you.
Finally. Again. DO NOT put the father on the birth certificate!