THANKSYour button is a genuine US Navy uniform button made during the War-of-1812 era. I understand your concern due to finding it at a location with no known Navy presence, but you can relax, it's definitely 100%-authentic, not a Reproduction.
Best theory for how it got to where you found it:
We know with certainty that uniformed personnel wore their uniform "back home" -- and sometimes, even after their term-of-service ended. For example, we find Confederate uniform buttons far from any civil war Military activity, at long-gone house sites which past-owner-research shows was once the dwelling of a Confederate soldier.
My most-favorite example of that is a vanished-house site about 30 miles west of Wilmington NC. A coin-hunter found dozens of very rare civil war British-made "Manuscript I" and "Lined I" Confederate Infantry buttons scattered in all directions around the house's foundation. But, absolutely no other civil war military relics were found, not even bullets... except for a few very small items like musket percussion-caps. Turned out the son of the house's owner was a member of the garrison at Fort Fisher during the civil war. Because there was no fresh water within miles of the fort, apparently the son brought his infantry-company's laundry home occasionally, and after washing it his mon draped it over bushes all around the house to dry. That explains how the buttons were found very widely scattered around the yard, in every direction. The percussion-caps and other small relics came from the uniform's pockets.