While the PRUSSIAN - OPTTOMAN connection is a bit of interesting History, I would say that it is a 7th Arkansas Corps badge, that was carved by someone of Prussian decent who was in that unit, or at least had acquired a Prussian coin.
The reason being, is that the points of the star, line up perfectly with modern day depictions of the 7th Arkansas Corps insignia.
If I had a guess, I would think that it was done by a member of th e 7th Arkansas, as a bit of camp craft. He likely wore it around his neck as a medalion, as Larry IL pointed out that it has a worn, elongated loop at the top.
There is an insignia, reputed to be of the 7th Arkansas, found by a MD-er over near Springfield. I have my doubts as to if it is truly 7th Corps Arkansas. Note that the star inside it is not at all like that of Deno's find, nor, of the known 7th Corps insignias. The points on this one is all wrong.
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The points look a lot like that of a Louisiana hat badge that was found.
Note that the modern day police badge for the city of New Orleans is the exact replica of the find near Springfield, Mo, points on the star, inside the Cresent positioned the same.
So, in my opinion, Deno found the real deal, a Arkansas 7th Corps badge, of probable camp craft orgin, and the guy in Springfield, Mo has a very interesting find, but not likely 7th Corps
Springfield, Mo find Not 7th Arkansas ...........................to compare... we have this dug LOUISIANA hat badge. It Looks like one to the left
The BOTTOM LEFT photo.... is the insignia flag of the New Orleans Police Department. It looks like the Louisiana Hat Badge, and the one found in Springfield, MO. The BOTTOM RIGHT is the Arkansas 7th Corps insignia. which, in looking at the star poiints, is identical to the the badge that Deno found.