In a finical manner; with excessive attention to small details or in a fussy, particular way.
From finical (adjective) plus -ly suffix forming adverbs. This creates an adverbial form describing how someone acts or performs an action in a particular or fussy way.
The -ly suffix is one of English's greatest inventions—it lets us instantly turn any adjective into an adverb, which is why we can describe someone 'finically' arranging their desk even though nobody used this word before the 1600s!
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