I am a single mother currently receiving public assistance. The father of my child is not listed on the birth certificate. Made it very cear to methat he had interest to be a part of the baby since learned of the pregnancy. Can I try to gain full custody of my child? Or is this a problem since I apply for public assistance because of being unemployeed in the state of California? Please advice

You already have full custody of your child

If you are applying for public assistance, you will be required to name the father or possible fathers so that the state may attempt to recoup their costs through the collection of child support. If you are currently unemployed and need state benefits, you should certainly be filing for child support as well.

As Jennie mentioned you already have full custody. Your child only has one legal parent right now. If he should decide that he wants to have visitation in the future, not being on the birth certificate will not stop him,he simply has to go through the extra step establishing his paternity through the courts. A court will make a decision at that point.