The first ever sidearm used by the United States military was the Flintlock pistol Model of 1775. It was literally just an American-made clone of the British 1760, which meant that in the Revolutionary War the British and American Continental forces wielded the same pistols against one another.
Specifically, the Model 1775 was a .62 caliber flintlock with a smoothbore barrel. It was well known for its accuracy and became the standard sidearm for officers. All in all, over 2,000 Model 1775 pistols were issued during the Revolutionary War, and thousands more were made and issued to the American military up until the invention and widespread use of of the revolver in the 1830s and 1840s.