This is a pin, possibly the type worn on a lapel or overseas cap. It may be what is called a distinguished unit insignia pin. It has two prongs on the back with spring-loaded clutches to hold the pin in place.
It’s about an inch tall, in the shape of a shield, and displays a white, five-pointed star on a black field. Inside the star is an Indian head in profile, with full feather headdress.
Frankly, I don’t even know whether it’s military, and if so what period.
Any help appreciated.
JT