There is a word, somewhere in my dictionary, that means a joke that only a particular group understands i.e., in-joke. I can't remember it and have failed to find it with an online thesaurus, but it is particular to the idea of a joke and not just secret knowledge such as arcane or esoteric.
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A bit of humor understood only by a particular group of people is variously called a private joke, inside joke, in-joke, or in joke, roughly in order of usage.
Private joke looks to be the oldest form, with many 19th-Century uses like this one (1890):
The three variants of inside joke become common around the 1960s. (In joke is common before that, but earlier uses mean “in jest” rather than “private joke.”)