If you are correct that the non-custodial parent is receiving Supplemental Security Income (SSI) and not Social Security disability (SSDI) (often confused with SSI) then there are no additional SSI benefits for the child.
Whether child support can be ordered will be a matter of your state's Child Support Guidelines and your state court case.
Best wishes for an outcome you can accept, and please remember to designate a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.
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