A US Large Cent dated 1797 would be a Draped Bust cent. Type this info into your search box and click images.
The US coin looks very much like a modern US penny
It is silver
More information is needed - is it a British penny or American cent? Please post a new, separate question with the name of the country that issued the coin.
A US cent dated 1913 is a Lincoln cent and the word Liberty is also on the front of the coin.
Please look at the coin again. No US quarters were struck in 1797 and the Washington series started in 1932. Post new question.
The British "Cartwheel Penny" and "Cartwheel TwoPence" were only issued in 1797. The Isle of Man "Cartwheel Penny" and "Cartwheel Halfpenny" were issued in 1798 and 1813. Any of these coins in excellent condition could be considered valuable.
They look like a shiny gold. But they are copper. So don't flip out. The most produced one is the 1797-1801.
On the reverse look at the knot in the ribbon that binds the wreath. If it has stems they will extend from the knot, one pointing to the last A in America the other to the U in United.
It looks exactly the same as the 2010 or 2012 penny.
The US coin looks very much like a modern US penny
It is silver
0.01
If you refer to the British 1797 Penny and Twopence coins, they may have been cursed by the people who had to use them. Both coins were very big and very heavy, even by the standards of the day. The 1797 "Cartwheel" Penny weighed 1 ounce or 28.35 grams and was 36 mm in diameter. The 1797 "Cartwheel" Twopence weighed 2 ounces or 56.7 grams and was 41 mm in diameter.
The British 1797 "Cartwheel" Proof Penny was minted in a variety of metals including, Gilt copper, Copper, Bronzed, Silver and Gold. Mintage figures are not given since coins from this period were usually produced by a specific weight, ie. two tonnes of Pennies. Most of the 1797 Proof coins are rated as various degrees of "rare".
The only British copper coins minted in 1797 were the Cartwheel Penny and the Cartwheel Twopence. They were referred to as "Cartwheel" coins because of the distinctive rim around the edge of the coins giving the appearance of a cartwheel. Exact mintage figures can only be guessed at since the mintage for 1797 was referred to in tons of coins. There was a combined mintage of 5 tons of British Penny and Twopence coins minted in 1797. These were the first British copper coins to have been minted in over 20 years. The 1797 Penny weighed 1 ounce or 28.35 grams. The 1797 Twopence weighed 2 ounces or 56.7 grams.
More information is needed - is it a British penny or American cent? Please post a new, separate question with the name of the country that issued the coin.
All British Pennies from 1982 to 2008 look pretty much the same as the Penny shown at the link below.