Welcome to Tnet! I grew up at Chazy Landing. The buttons look American military from the War of 1812 but could be civilian from that era. I can’t identify the design.
Seriously great finds!!! Congrats! I was up at pound the ground last fall and was hoping to find some 1812... I was not successful but some other people were. Great area for that! Those buttons look like they are pewter? Make sure to do some kind of preservation... but ask an expert I'm no expert!