Wrongfully and Wrongly

adverb

• In an unjust or unfair manner.
  • usage: "the employee claimed that she was wrongfully dismissed"; "people who were wrongfully imprisoned should be released"

adverb

• Without justice or fairness. "wouldst not play false and yet would wrongly win- Shakespeare
• In an inaccurate manner.
  • usage: "he decided to reveal the details only after other sources had reported them incorrectly"; "she guessed wrong"
  • synonyms: incorrectly, wrong

(adv.) In a wrong manner; unjustly; erroneously; wrong; amiss; as, he judges wrongly of my motives.