WA state child custody laws, who has more rights to primary child custody, mother or father

If the father wants to file a petition to determine paternity, he likely has that right.

The court will determine paternity and if needed, determine who will have custody of the child.

Assuming the court determines the father is the legal father, unless the court finds the father to be unfit as a parent or otherwise living with the father would not be in the best interest of the child, the court likely will order that the child lives with the father since the mother is in prison.

You likely should review your facts and options with an attorney.