Which American frigate was captured by the British in January 1815?

The American frigate captured by the British in January 1815 was USS President.

Commanded by Commodore Stephen Decatur, President attempted to escape the British blockade of New York Harbor on 14 January 1815. The ship ran aground briefly while leaving port, damaging its hull and reducing its speed. A British squadron then pursued and engaged it. After a fierce exchange with HMS Endymion, President was forced to surrender on 15 January.

The capture was one of the last major naval actions of the War of 1812. President had been a valuable and heavily armed United States frigate, nominally carrying 44 guns, and had already taken part in several wartime cruises. The British considered it an important prize and commissioned it as HMS President, later rating it as a 50- and then 60-gun ship.

This answer is sometimes confused with USS Constitution, which famously defeated British warships during the conflict, or USS Chesapeake, captured in 1813. President was broken up by the Royal Navy in 1818.