You haven't indicated where the property is located, but assuming it is in the U.S., ownership rights to real property (including mineral rights) can be inherited along with other assets within a decedent's estate. You have two issues that need to be resolved before you can determine whether your father owns such rights: (1) Whether your grandfather owned these mineral rights at the time of his death; and (2) whether these rights were passed to your father via a will, trust, or intestate succession. Real property conveyances must be in writing and recorded with the county recorder's office where the property is located. A search of these records should answer the question as to whether the mineral rights were conveyed in the inital land sale or at some later time. A lawyer specializing in real property can do this title search for you if you do not know the process. Assuming the mineral rights still belonged to your grandfather at the time of his death, you then must determine if those mineral rights were bequeathed to your father in a will or some other instrument, or passed to him by operation of law (via intestate succession). If so, I believe that a probate proceeding will need to be opened (or re-opened if the estate has already been distributed through a probate proceeding) so a judge can order that title to the mineral rights be transferred to your father's name.

If the mineral rights were never sold apart from the actual land, then whomever owns the land owns the mineral rights. It is pretty unusual today for individuals to own the mineral rights to their land. You can go to the court house and look at all of the deeds and transfers.