What are the general custody rights to a father of a newborn?

They are very general for all cases. They have to be inforced by a court judgment awarding visitation guidelines. As a newborn, the visitation would probably be a few hours here and there certain days of the week. As the child ages they time allotment would progess in time and overnight visits. Unless you think the child would be in danger they should be encouraged to have a relationship with their father. You would only be harming the child by isolating the relationship.

I live in Va and my husband is a convicted felon. We have been separated since Nov of 09 and he lives with his married girlfriend in an apartment he isn't supposed to be in. I am 8 months pregnant with our daughter and he is now wanted to take me to court for custody. I need to know if has any legal barrings to do so? Any information would be greatly appreciated.

I need to know if has any legal barrings to do so?

Yes, you both have shared parental rights. You need to go to court to get the court to delineate each of your custody, visitation, and child support rights and obligations.

Children born in the common wealth to a married couple are presumed to be the offspring of the husband... Thus if you were not married when the child was born... hmmm

I... I am 8 months pregnant with our daughter and he is now wanted to take me to court for custody. I need to know if has any legal barrings to do so? ...

My earlier answer applied to the child who has already been born. He can't go for custody of an unborn child until she is born.