A minor was a secondary field of study.
In 1996, noting Tom Paris's familiarity with obscure horror films, Rain Robinson quipped, "Let me guess. You minored in B-movies." (VOY: "Future's End")
In the 2370s, Raffaela Musiker minored in Romulan Relations at Starfleet Academy, with a major in intelligence. (PIC: "The Next Generation")