I have looked through my references and can't find a match for your button. The front is similar to some 1 piece buttons but nothing I saw in two piece ones was even close. Maybe someone can ID it for you.
Your find at the pre-civil-war fort is a slight variation of button number R-16 "Regiment of Infantry" US Army button in the Albert button-book, shown in the photo at the top left on page 31. Unlike almost all other US Army buttons, the R-16 through R-32 buttons had the Regiment number stamped into the button's face after it was made. Your button having a plain blank shield (no number) indicates it was not issued by the US Army... but was instead sold by the manufacturer as a "leftover" to a State or Local Militia unit.
Time-dating for your button:
Sorry, but I have to disagree with Dfxcobb's opinion that it is a "pre civil war 1798-1802 militia" button, because...no American Military eagle-with-shield brass TWO-PIECE buttons were manufactured before the 1830s.
You asked whether it is a kepi-hat chinstrap button or a uniform button. But you did not tell us its size, so I cannot answer that question. All I can tell you is, American kepi buttons tended to be 12mm to 14mm... a bit smaller than the cuff-size buttons. That being said... sometimes cuff buttons were used on a kepi chinstrap instead of the "correct" size button.
Update:
After I posted, you replied that the button's diameter is 12mm, which means it is definitely a kepi-hat chinstrap button.