Its not fair that because father is getting ssi he doesn't have to pay child support. So basically he gets off with paying nothing. How does that work? What about the help with the mother?

Had the father worked in the past? If he is on SSDi then the child may be entitled to benefit. If he is on straight SSI then the child receives no benefit as he didn't work long enough to qualify for it. SSI is a minimal amount to live from.