In error, erroneously, mistakenly.

So as to cause an intended object to be missed; (with reference to physical aiming or directing of something) in the wrong direction, or on the…

Wrongly, erroneously, wickedly.

Modifying a verb: out of place, beside the mark, amiss; (later) spec. in a manner that goes beyond what is normal or accepted; oddly, unusually…

In an erroneous manner. In a misguided manner, under the influence of error.

Foolishly, carelessly, wrongly.

In a mistaken manner; by mistake; under a misapprehension; erroneously.

by (rarely from, †in a) mistake: erroneously, mistakenly, in error. in mistake for: in error for.