What rights do fathers have when they dont help with the care of a child?

I am the single mother of a little boy who has down syndrome and a terminal heart defect. It was all to much for his father to stick around. since separating he never sees his son nor pay child support. He has a good job that pays $1200 a week cash. I have not been able to go back to work as our son is in and out of hospital all the time and he needs my care constantly as he is a fussy eater and needs things that only i can understand. leaving him in daycare is not an option as not only is he very attached to me i am scared that he will get sick from one of the other children. His father never sees him but has contacted me recently about seeing him. I want this as every mother needs a break. But i am bitter about him not helping financially. I dont want to keep my son from his dad but I am the one who loves my boy I am the one who has been there from the start never leaving his side through his heart operations and hospital stays. WHAT DO I DO. he says why should he pay child support when he doesnt get to see him. but he is the one who moved 2 hours away. its his choice not seeing him not mine. Ive never stopped him but im at that point