My ex doesn't want me to be in the birth certificate of our child ( 3 months old), but she wants money from me on a weekly basis. Also she doesn't allow me to take the baby home for me to spend timw with him she only wants me to come over her house. What can I do?

Go to court and have visitation rights legally established and a schedule set... what she can get away with now with the child as an infant she won't be able to very soon as it gets a little older.

Your ex has no choice in the matter if you are the father. As smoothy said, you go to court, establish paternity, have the birth certificate amended, get a reasonable visitation schedule as well as court ordered child support. As the father you have pretty much the same rights as she does, but you will have to go to court to enforce those rights.