Can a 24 year old child who finds out who her biological father is, eligible for proceeds of father's estate?

First, any question on law should be in the Law forums (this was moved from Children). Second any question on law needs to include a general location as laws vary by area.

If the father leaves a will that excludes the child, IF the child can prove the father din't know about the child, they MIGHT (long shot) get a share. If the father dies intestate, the child MIGHT get a share if they can prove a blood relationship.

Depends on what his will says. If he had a will and did not include you as an heir then it will be difficult, although if he did not know of your existence it may be possible to argue that you deserve some portion. If he had no will (i.e. he died intestate) then depending on the state where he lived and what other living relatives he had you may be entitled to a portion. In either case you will have to show that you are indeed his daughter, as I assume that his name is not listed as the father on your birth certificate, right? You should consult with a lawyer to help determine whether either of these would possibly apply.