Father not on child’s birth certificate

We are separating and bc of complications he was not at the birth. I’m about to move out with our baby and need to know what steps I need to take next to get him on the birth certificate. He honestly believes that once we go he will have no responsibility toward our child and has even said “how do I even know he’s mine” which absolutely broke my heart. I need some direction ladies.. how do I tell him my “demands” or needs without sounding needy or pathetic? Help 😔 if I say outright that he needs to give me money to support the baby he will say I’m trying to trap him. We’ve been together for 5 years and our child is 10 months old.

He says I won’t get anything bc he is in school and takes out student loans to pay for it. He told me I’m petty bc he can’t afford it. I have no job and have been a stay at home mom for years.. hello!!?