Dialect or archaic term for lice, small insects, or parasites associated with apples or apple storage; possibly apple seeds humorously compared to lice.
From 'apple' plus 'snits' (plural of snit, meaning a state of agitation, or possibly connected to 'snit' as tiny insect). This appears to be dialectal English, possibly playful or children's language.
Medieval English loved insulting compound words—calling someone 'applesnits' combined the idea of worthless parasites with the lowly apple-seller, creating memorable workplace insults!
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