Not affiliated with the government
Aside from SSI, which can provide support for disabled children in needy families, or survivor benefits when a parent dies, I am unaware of a "child support" from the Social Security Administration.
You may want to explore TANF (Temporary Assistance for Needy Families) which may help. TANF is generally administered on the state level. For example, here is information about TANF in Texas :
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