It's unknown how a player earned this patch. And, based exclusively on its chevron shape at the top, the design suggests that it was intended to fit with the other 3- and 4-patch chevron sets that Duncan made.
When you earned this particular patch is also unknown. It may have been the last one you earned. Or, you earned this patch for winning the contest, along with earning either your first 5-trick or 8-trick award patch. The latter theory is more likely. When the National Yo-Yo company held contests, you first earned the 5 trick patch based exclusively on your own yo-yoing skills. If you won the competitive contest between other kids, you also earned the National Yo-Yo Champion patch at the same time.
This patch design first came out in the late 50s and was used into the early 60s. Interestingly, starting in the early 50s and with each successive year thereafter—until the early 1960s—Duncan patch sizes progressively got smaller. This patch set appears to fit into that reduced size time frame of the early 60s.
