Does and illegal immigrant still have rights to see his child even though he owes thousands in child support?

im in a current situation where my exhusband is an illegal immigrant (i didnt know he was until i was 6 months pregnant with our child, i was in High School). as of 2010 he has only paid 100 dollars of child support and refuses to give me money for our daughter. he wants to see her and i have even though he told me he wasnt working and he couldnt give me any CS. well i found out that he is working( illegally of course) and i decided to deny him rights to see her.