In a fetching manner; in a way that is attractive, charming, or appealing.
From fetching (attractive, appealing) + -ly (adverb-forming suffix). Fetching itself comes from the idea of something that 'fetches' or attracts attention and admiration.
While 'fetching' (an adjective meaning attractive) is fairly common, 'fetchingly' is rarely used in modern English because we usually say 'attractively' or 'charmingly' instead. It's a ghost word—grammatically correct but practically obsolete.
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