Receiving money from the government for being Indian ? Gosh, I seem to have missed out on that one ! And so did my ancestors !
Sadly, it's become something of an Internet Myth, along with a whole bunch of "mythology" promoted on this and numerous other forums and boards by people who have no American Indian ancestry whatsoever.
Anyway, your family is well documented in Federal Records back to at least 1840 as Free White Citizens of the United States as residents of Page County, Virginia.
Not sure where the Mohawk idea came from ? They never resided anywhere near Virginia !