Hamilton was the leader of the Federalist Party.
In its very earliest days, yes, along with John Adams and John Jay. So to be exactly precise you’re correct. But the Federalists were more a faction that believed in a stronger central national government and the last time they occupied the still-under-construction-and-not-yet-white White House was in 1801. But the dividing lines were fluid. For example, Madison was one author of the Federalist Papers, but also a founder with Jefferson of the Democratic Republican Party (ancestors of today’s Democrats).