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.

I don't have a good photo or scan of a genuine vintage example of this patch so I'm unable to put an image of the patch design itself here. A number of replicas of this patch design have been made over the years, but one that is apparently a very faithful replica of the original is currently available from John Berry here.