United States Navy. Emblem specified by a US Naval Department order on October 26, 1798, "an eagle, with shield on [its] left wing, enclosing a foul anchor." A followup order in 1802 specified that the eagle be encircled by stars.
Your button's 13 statrs and the backmark saying "No. 4 Spies/JM/ Treble Gilt" means your button is NA-44Bv in the Albert button-book. The "Spies" in the backmark is Adam W. Spies, of Birmingham England, but also with a branch office in New York City. Spies was in the button business only from 1827 to 1835, which conclusively dates your button to those years.