Yes the child's father owes you child support whether or not you are married to another man. If he is unemployed it will be harder to collect. The County Family Support Division can assist you with child support collection free of charge.
Also the amount of support for your child will be less if the father proves he is supporting a second child by a different mother.
This question is intended to be a summary of relevant California law where this attorney is admitted. It is not a complete answer or researched legal opinion. It is the policy of this firm to enter into a written fee agreement with all clients, and this answer does not create an attorney