How do I request paternity test? There are 2 children, 1 I do have questions on, the mother has recently been awarded full custody and now I'm being

You do not provide enough details to understand where in the process you might be.  If you have not looked at the forms on the self-help center website you should; at the very least, show up at the next scheduled hearing and indicate that you are not sure about paternity; that should result in a test being ordered. Your best bet, however, would be to have a consultation with counsel in advance.  To answer your question -- maybe -- generally, you do not own child support for children that are not yours, but a number of facts could lead to some different result.