In a dampish manner; in a way that is somewhat moist or damp.
From 'dampish' plus the adverb-forming suffix '-ly,' creating an adverbial form that describes how something is done or exists in a dampish way.
English speakers will add '-ly' to almost anything to make it an adverb—you could say the room smells 'dampishly' to describe that vague damp smell, even if it's not a word most people know!
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