If you are the "parent" that was given custody of a child, then the answer is "yes", you certainly can. However, if you never got legal custody of a child, and the mother left you with the child, you should seek custody first, then try to gain child support. These things are usually the purview of the state in which you live (if you are in the US). You really should get the advice and counsel of an attorney. If you really cannot afford one, some states will have "legal aid" centers that you could access. Not all states have that, however.
