I have my kids 50% of the time their mom has them 50% of the time. Neither of us pay child support because we equally support them. I am now going to get SSI for myself as well as my two kids. I want to know if my ex (we were never married) can attempt to get some of the SSI. We have shared joint custody of the kids.

How was your child support agreement figured in the first place? We you both working and now your income has dropped a lot? If so then you should receive the checks for the children. At worst case you would split the monies but I don't see that happening.

Is your child support and child custody court ordered ? Depending on the state, even with 50/50 one party can still pay child support depending on each parents income

The mother orf course ( as you can) always go back to court to ask for a modifications to your original order.

Of course the children can receive SSI benefits if you are.