Look up coin dealers in your area and try one of them. A reputable coin dealer will confirm your coin as genuine and give you a valuation and maybe an offer to purchase it from you.
Alternatively, try eBay.
There were only two British "Britannia" coins minted in 1797, one was the copper Cartwheel Twopence at 41mm in diameter, the other was the copper Cartwheel Penny at 36mm in diameter. They are identical except for the size. See the link below.
The British issued "cartwheel" Pennies and Twopences in 1797 only.
Apart from George III, the only person depicted on British 1797 coins is Britannia, the female personification of Britain. She is usually shown as being seated and holding a trident and shield. In 1797 she is on the reverse of the "Cartwheel" Twopence and the "Cartwheel" Penny.
If you refer to the GEORGE III 1797 "Cartwheel" Penny and Twopence, they are both made from copper and are of almost identical appearance, the Penny is a little over 30 mm in diameter and the Twopence is much larger at about 40 mm in diameter.
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.
Your coin is either a British 1797 "Cartwheel" Twopence 41mm in diameter, or a British 1797 "Cartwheel" Penny 36mm in diameter. If somebody has drilled a hole in it, it might be worth a few Pence. Modified coins have no collector value.
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.
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 only George III coins with Britannia on the reverse are the Twopence, Penny, Halfpenny and the Farthing, but none of them had a milled edge. From 1797, the Penny was 36mm in diameter, the Twopence was 41mm in diameter and both coins were made from copper.
A British 1797 copper Twopence (George III)(41 mm diameter, aka a "Cartwheel coin"), uncirculated and in absolute mint condition could fetch up to £1,400 GBP (it would have to possess close to or full original red mint lustre to command this price). If it has been circulated but still in good condition, it might fetch anything from £40 to £400 GBP. A British 1797 Twopence (Copper Proof FDC) could fetch up to £900 GBP. A British 1797 Twopence (Bronzed Proof FDC) could fetch up to £800 GBP. A British 1797 Twopence (Silver Proof FDC) could fetch up to £8,000 GBP. A British 1797 Twopence (Gold Proof FDC) could fetch up to £15,000 GBP. A British 1797 Twopence (Gilt copper FDC) could fetch up to £1,750 GBP. NOTE - The reverse of these coins is upside down to the obverse. This is normal. Remember, these coins were struck in large numbers 722,160 for the standard copper 'currency' coin. The proofs are very rare and highly sought after. The values quoted are the best possible for the best specimens in their grades, but may be significantly lower due to varying demand for the coin and the prevailing economic climate. A reputable coin dealer will be able to give a more accurate valuation based on inspection of the coin.
British George III coins dated 1797 include -GoldGuinea - Crowned spade shaped shield on reverse - 24 mm in diameterHalf-Guinea - Crowned spade shaped shield on reverse - 21 mm in diameterThird-Guinea - Crown on reverse - 17 mm in diameterSilverThere were no silver coins minted in 1797.CopperTwopence - (Cartwheel) Britannia on reverse - 41 mm in diameterPenny - (Cartwheel) Britannia on reverse - 36 mm in diameterPlease determine which you have and ask a more specific question.
British coins issued in 1797 included - Gold Guinea Half-Guinea Third-Guinea Silver none Copper "Cartwheel" Twopence "Cartwheel" Penny Due to Britains ongoing expenses with various wars in the late 18th and early 19th centuries, there were very few silver or copper coins minted, subsequently there were a great many privately minted tokens produced.