What is the value of a 1797 Carson City coin?

The Carson City Mint did not open until the 1870s. In fact, Nevada was part of the Spanish Empire in 1797 so it could not have had a U.S. mint regardless.

Please check your coin again and post a new question if the date or mint mark is different.

Also, be aware that especially if it's a dollar or half-dollar, there has been a flood of counterfeits over the last couple of decades. Most are made in the Far East; some are very good and others are laughably bad with impossible dates, designs, or mint marks. For ex., a couple of years ago I saw a purported "rare Washington quarter" with the date 1865! There was just one Word for it - FAKE.