You could file an objection or challenge to the distribution of his estate (assuming the estate is still "open" and has not been fully resolved and settled--once it is, it is generally too late to challenge who received what) and, in the course of so doing, will have to provide proof that you are his son. (Living with him is largely irrelevant; you'd have to show the biological connection or that you were legally adopted.) That might require having to have a DNA expert who conducted a DNA test testify in court, if that is your proof.
This could be an expensive and complex case to bring: if there are few assets, it's not worthwhile; and if your father's estate was large, expect that whomever else is inheriting to fight you aggressively on this, to make sure you don't get any part of their "share." Consider carefully whether it's worthwhile doing; a good idea would be to consult to with a probate attorney about the case, to understand the odds of winning, the cost, the challenges, etc. If it's not worth consulting with an attorney, it's likely not worth pursuing.
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