If your relative laid “claim” to a piece of property, what documents might have been generated as a result?
Did he pay taxes on it before the title was actually clear? Did he have to find a land claim or some sort to obtain title to the property? If so, before the American Revolution the place to look for land claim records are at the appropriate state archives. Land claims after the Revolution are at the National Archives. It’s possible that your relative filed a pre-emption claim if he settled on property in the federal domain. That’s a federal land record and the completed claim would have generated a patent. The process for completing a pre-emption claim is different from that of filing a homestead claim.
If your relative signed a quit-claim deed he was giving up his claim to the property and may have had legal title to the property in question or he may not. A quit-claim deed merely indicated that his claim was being given up and transferred to another person.
And if you ancestor had a different type of claim, perhaps to other property, there may be a court record documenting his attempts to clarify that claim.