Legally,
You can not get out of the lease ( even paying) unless landlord and boyfriend agree, boyfriend is part of that lease also and does not have o agree to take anyone off.
So you are not going to get your name off lease.
You do need to inform the landlord that you are moving out and that you will not renew your name on the lease after April. If you don't inform him of that, you could even be stuck on the renewal.
The boyfriend can sue you for your share of the lease, but if you are being abused, who cases, move out. He will either sue you or not sue you, I would not worry about the money.
You are wrong on the child visitation. Forcing him to pay has nothing to do with his rights to visit. He may go to court and ask for Joint Custody, Visitation any time he wants, His paying or not paying child support has nothing to do with his rights to visit.
So you need to get to court ASAP and get a order of custody for the child giving you custody, and asking for support.
Most states in the US have legal aid society that can help you with the paper work, some family courts have fill in the blank forms I am told. It is not at least in GA totally free, there are filing charges of about 100 dollars. But as noted if he is on the birth certificate or has proven paternity, he has as much right now, as you do, to have the child, So you need to get a custody order in place
