Hi Steve,   Here's more information about the Muskogee Army Air Field, it's exact location and some history. https://www.okhistory.org/publications/enc/entry?entry=DA016

Further research revealed the 13th Infantry Division's engineer regiment was the 213th Engineer Regiment. Could this shoulder patch been adopted and unofficially worn by the 213th Engineer Regiment? Could they have abbreviated their numerical designation to that of "13" to coincide with the numerical title of their parent organization - the 13th Engineer Regiment? and designed a shoulder patch that copied certain design elements found in the regimental shoulder patch, such as the circular shape - the black cat, as well as the numeral "13", while replacing the upside-down horseshoe with an engineer's castle?   Is this just a coincidence?   Does anyone have any thoughts or opinions regarding the identity of this, as yet, unidentified AEF shoulder patch?   I'll close with the portrait of the above Doughboy in civilian clothing.    

Those are some nice photos Matt, but I don't recognize anyone of the "higher ups" in it. Where was this base located in relation to Muskogee? I've actually been to Muskogee eons ago and don't remember seeing anything there about it. Neat history on the 41st with the Balloon Co. start in 1917.  Thanks for the post.     Steve

While researching the photo and the shoulder patch, the black cat reminded me of the 13th Infantry Division's shoulder patch which also prominently featured a black cat as part of its design. Here the 13th Infantry Division's black cat patch is compared to the above 13th Engineer Regiment's black cat patch.        

it's a box that I have and not a button

Larger views of the "castle and cat" shoulder patches. Note that the numeral "13" shown in the center of the patch in the first photo has been washed out in both of the below images. I have posted the first photo again, showing the numeral "13" for comparison.    

Wow, i missed this one big time! Very nice looking RIA!  You might look for the bolt steel lot code at the front of the safety lug, it could be a D1 or a C13. If you don't find anything there, the bolt may have been replaced at some point. I don't think the engraved S/N on the bolt means it's a Greek returned rifle, to me it indicates that it was marked just to keep that bolt with that rifle for correct headspace. I would say that the stock has been refinished by the faint P proofmark, is there any evidence of a cartouche on the stock?  Most RIA rifles of that era had the CN(Conrad Nelson) stamp.  You also have a very nice SA bayonet and early scabbard. An early sling, front sight cover and a cleaning kit would complete this good looking outfit. Keep looking! Thanks for showing this.     Steve

I do not think it is military. This is on EBay.

Closer looks at the soldier    

Before I go any further, I should post the two photos that I obtained showing the mystery engineer patch with a black cat.