The southern state that Britain gained as a result of the war (American Revolutionary War) was Georgia. The British implemented a Southern Strategy during the war which led to the capture of Georgia's major port, Savannah, in December 1778. They regained political control in Georgia, forcing inhabitants to swear allegiance to the king and forming Loyalist regiments. This was part of a broader British campaign in the southern colonies aimed at securing Loyalist support, which initially had some success but ultimately failed with the British defeat at Yorktown in 1781.
So, the key southern state gained by Britain during the war was Georgia.