No song with that title has charted.
You may be thinking of Money (That's what I want) by Barrett Strong 1960
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Eddie Holland sang "Jamie" in 1962
Mama said-The Shirelles, a '60s group
sorry, I can't find any sixties versions, however here are three close ones Roger Williams 1958, Jerry Lee Lewis 1959, Andy Williams 1959
Strawberry Fair is an English Folk song by H. Fleetwood Sheppard in 1891. A version was recorded by Anthony Newley in 1960. The beginning is the same as the traditional version, but then the rest is altered for humorous effect.
Frankie Valli sang with the group 'The Four Seasons' and it was early 60s pop music.