From Wikipedia:
"My Boy Lollipop" is a song written in the mid-1950s by Morris Levy (under the pseudonym "Robert Spencer") and Johnny Roberts. It was originally recorded by the American singer Barbie Gaye and became a minor Rhythm & Blues hit in late 1956, spelled "My Boy Lollypop" (with a y") on the original 78 record label. It is most famous, however, for the 1964 recording by Jamaican singer Millie Small which became an international hit.
The Millie Small version
The song was discovered by Chris Blackwell, who was trying to find songs for Millie Small to record. Millie's version was recorded in a ska/bluebeat-style, and became her breakthrough blockbuster hit in Britain, reaching #2. It also went to #1 in Ireland and #2 in America. "My Boy Lollipop" was one of the few international ska hits and was the first record to help Blackwell's Jamaican label, Island, make millions. It remains one of the best-selling reggae/ska hits.
The record's arrangement is credited to Ernest Ranglin, who also plays guitar on the recording. A persistent rumor claims the not yet famous Rod Stewart performed the harmonica solo on the recording; Jimmy Powell has claimed he was the performer [1], but many who have looked into the question say that the instrument was played by Pete Hogman of The Five Dimensions.