I pay child support but have just found out that said child is drawing ssi. Do I have to pay child support other than the arrears that has accused over the last few years?

It depends on what the court says. This depends on proportions and other things that only a court can do. You can go to jail and have your license suspended for not paying child support.

You have to pay what the court orders. Any income the child receives from SSI or other sources will probably not have a bearing on your support obligation.

If you think it should, then go back to court and ask for a modification of the current support order. Until the court changes the order, you pay what the court has ordered. If you have accrued arrears you have to pay those as well.