As can be seen in the photos above the Gemini 3 crew did not wear an emroidered mission patch during the flight.
It was only some time after the mission itself that a "Molly Brown" patch, based on the design shown on the right, was created and used by Young and Grissom on their NASA flight suits. The image on the right shows an example on Young's flight jacket as displayed in the Astronaut Hall of Fame (photo courtesy of Andrew Li).
It's not clear how many patches Grissom and Young had made for their own personal use but they were certainly never made available to the general public and are extremely rare today. A couple of nice replicas have been produced over the years, with one still
on sale today.