Originally recorded (as “I’ve Got My Mind Set On You”) by James Ray (1962).
Hit version by George Harrison (US #1/UK #2/AUS #1 1988).
From the wiki: “‘I’ve Got My Mind Set on You’ was written by Rudy Clark and originally recorded by James Ray in 1962. Standing just 5′ tall, Ray first recorded as Little Jimmy Ray. He recorded ‘Make Her Mine’ in 1959, but it was unsuccessful and by 1961 Ray was destitute and living on a rooftop, though still performing in clubs.
“Songwriter Rudy Clark befriended him, and persuaded Gerry Granahan of Caprice Records to sign him. Using the name James Ray, his first recording was of Clark’s song, ‘If You Gotta Make a Fool of Somebody’. The record was a hit on both the Pop and R&B charts. The single was issued in the UK in 1962 as well, and the song was performed by The Beatles before being discovered by Freddie and the Dreamers, who took their cover of it into the UK Top 5 the year after.