It appears that this patch was produced as an expansion to the original Eagle One Aerospace Mercury patch series.
Mercury-Atlas 10 (MA-10) was a cancelled early manned space mission, which would have been the last flight in NASA's Mercury program. It was planned as a three-day extended mission, to launch in late 1963; the spacecraft, Freedom 7-II, would have been flown by Alan Shepard, a veteran of the suborbital Mercury-Redstone 3 mission in 1961. However, it was cancelled after the success of the one-day Mercury-Atlas 9 mission in May 1963, to allow NASA to focus its efforts on the more advanced two-man Gemini program.