Definition of wrongly adverb from the Oxford Advanced Learner's Dictionary

  

wrongly

 adverb
adverb
BrE BrE//ˈrɒŋli//
 
; NAmE NAmE//ˈrɔːŋli//
 
 
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in a way that is unfair, immoral or not correct She was wrongly accused of stealing. He assumed, wrongly, that she did not care. The sentence had been wrongly translated. They knew they had acted wrongly. Rightly or wrongly, they felt they should have been better informed (= I do not know whether they were right to feel this way). She was wrongly diagnosed as having skin cancer. Which Word?wrong / wrongly / wrongfully In informal language wrong can be used as an adverb instead of wrongly, when it means ‘incorrectly’ and comes after a verb or its object:My name was spelled wrong. I’m afraid you guessed wrong.Wrongly is used before a past participle or a that clause:My name was wrongly spelt. She guessed wrongly that he was a teacher. Wrongfully is usually used in a formal legal situation with words like convicted, dismissed and imprisoned.
See the Oxford Advanced American Dictionary entry: wrongly