There were no British Threepences minted in 1797, bronze or otherwise.
Other than Maundy coins, the only Threepences known to have been minted between 1786 and 1833 were the 1792, 1795 and 1800 coins.
There were no British Halfcrown coins minted from 1752 to 1815 inclusive.
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.
You have described every British coin issued in 1797. Please provide the type of metal it appears to be made from, the diameter of the coin, the inscriptions and the design on the reverse.
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.
For many years up to and including 1792, the British Penny was silver. From 1797 to 1860 inclusive, the Penny was copper. From 1860 until its last minting in 1967, the Penny was bronze. From 1971 to 1992 inclusive, the decimal (New) Penny was bronze. From 1992 to present, the decimal Penny has been made from copper plated steel. The only British decimal coins with any brass in the alloy are the One and Two Pound coins.
The British 1797 Penny does not have stars on it. 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 and counterfeit coins produced. To get an estimate of value on a privately minted token, you need to provide the details of the inscription on the token.
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.
1797
The British issued "cartwheel" Pennies and Twopences in 1797 only.
William Hale - British inventor - was born in 1797.
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".
To determine the equivalent value of a 1797 penny today, you can consider factors like inflation and historical purchasing power. A 1797 British penny, for example, would be worth roughly £1.50 to £2.00 in today's money, depending on the specific inflation calculation used. However, due to the differences in currency systems and economic conditions, this is a rough estimate and can vary based on various economic factors.