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Even if you could claim past child support, this was due your mother or guardian years ago and without a court adjudication, the would be impossible to ascertain and at age 37, you would no longer require support. With the changes in the law holding "deadbeat dads" more responsible for support it could be possible but very unlikely as statue of limitations problems with no past judgement.
At your father's death depending on whether he dies intestate or with a will, you might be due a portion of his estate. Unless you are disabled (there are also certain requirements for this), then you would not have access to any social security benefits because you are not a spouse or minor child in need of support. Unfortunately a portion of your father's estate seems like the only option for receiving any type of funds from your father. Even that could be unlikely if your father drafted a will or he died insolvent.
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