accidentally; by mistake; in error
Adverbial て-form used before a verb to say that an action happened unintentionally or because of an error. Often has a slightly formal or written feel compared with 間違って or うっかり.
I accidentally deleted the old file.
He got on the wrong train by mistake.
誤って is an adverbial phrase describing how an action was done, while 間違える is the everyday verb meaning to make a mistake or mix something up.
Standard kanji spelling for the adverbial expression meaning that something is done by mistake or accidentally.
Attested rare kanji form for あやまって; 誤って is the practical spelling for this word.
Grammatically the て-form of 誤る, meaning to make a mistake or err. The kanji 誤 is conventionally associated with error or mistaken action; the alternate 過って spelling is rare.