The earliest patent for the new US was Samuel Hopkins, of Philadelphia, Pennsylvania , on July 31, 1790, for " the making Pot ash and Pearl ash by a new Apparatus and Process." Sounds pretty dull, but it turned out to be rather important, as it meant that all the settlers on the frontier could burn wood and actually sell the ash. It became a significant business in the hinterlands.

But it is a bit tricky, because there were patents before there was a United States, and they were different kinds of patents, and it created a problem. The earliest US patent dispute hit the following year, in 1791,between John Fitch , John Stevens and James Rumsey over the rights to build steamboats. Fitch had gotten monopoly patents in some states, patents he'd written himself, which granted him the rights to any and all steamboat designs if he could himself show a working one within five years, and he did. But a monopoly patent promised a monopoly to someone who would do something important ( say, make a iron refinery) so they could get investors; it was a way for a government to try to develop a valuable industry. The new USA patent system only recognized novelty of design, and when Fitch tried to get a US patent, Rumsey and Stevens could complain that their steamboat designs had little to do with his. It was a terrible muddle, and the first US patent commission fumbled, ended up ( as far as we can tell) granting patents to all three for all the steamboats- in effect, not granting a patent to anyone for anything. It set back the development of the steamboat for decades.