For your consideration is a vintage, believe WW1 era, U.S. National Army pin.  I believe this to be the hat insignia.  It is a screw back pin with no markings.

I have recently acquired an estate with a lot of military pins, awards, etc.  The gentleman of the estate was in WW2 and his father was in WW1.  Items are listed as found.  I have not cleaned them.  Check my other listings for more from this estate as well as other vintage, antiques, collectibles, fabrics, clothing, holiday and more.