Urgent : Father of my child advise

So my I broke up with the father of my child last year as he always lied and was never there for appointments or even when I gave birth this year. He was using me for financial gain & sexual gain. I fell pregnant and he agreed to keep the baby. However he is not on the birth certificate as he wasn’t there and he’s happy about this. Fast forward last weekend after my baby was in hospital for breathing, that same day day my baby was discharged he came to visit our baby we had a disagreement all because he wanted to be intimate with me I said no. The next 2 days he didn’t even text to find out if he’s son was doing ok. When he came yesterday I asked him why he didn’t even check on his son he said he was angry with me this didn’t sit well with me. Also I left the room to take a phone call and my baby had a weird cry while the baby was sleeping in his hands … I ran and took my baby off him I wasn’t sure why our baby would cry like that as this never happened. Maybe I’m over thinking but I don’t know to trust him. I don’t know what steps to take… he says he wants to visit our baby 2 times a week instead of 1 which i agreed but my anxiety with him is so high I wish I could just do one day a week. I don’t trust him to leave the room with our baby… I don’t trust him as a whole… what steps do I take to make sure our baby is ok?