Mining rights were the legal rights to mine on a piece of property.
In 2372, Neelix suggested USS Voyager travel to the Hemikek system, where Hemikek IV, a planet rich in minerals whose mining rights were controlled by a non-aggressive consortium, could provide them with the necessary verterium and cortenum. (VOY: "Investigations")
In 2378, as part of an educational program for Q Junior, Chakotay had him attempt to settle a dispute over mining rights on a planetoid between the Nausicaans, Bolians, Cardassians, Romulans, Ferengi, and Bajorans. (VOY: "Q2")