Green’s Dictionary of Slang

Billy the Kid n.

[rhy. sl. = Yid n.1 ; plus the wearing of large, black, wide-brimmed hats seen as similar to a cowboy hat]

a very orthodox Jew.

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[UK] (ref. to 1930s) R. Barnes Coronation Cups and Jam Jars 96: Around 1928 [...] the slang words for Yid were ‘tea pot lid’, or ‘backward skid’, or ‘Billy the Kid’. The last name was only applied to the very orthodox Jews, the officer of the synagogue.