What is the value of a 1792 US quarter?

The first US quarters were dated 1796.

If you look more closely at your quarter (you did wonder how a 220+ year old quarter could look so shiny, right?) you'll see it has 2 dates. It's a modern state quarter. 1792 is the date its state was admitted to the union. The other date is the year it was minted.

That would be an impressive find, given that the U.S. Mint didn't begin production until 1793. If this quarter has George Washington on one side and Kentucky on the other, then it's a State quarter from 2001 and is worth 25 cents.