Right in a wrong way? Wrong! (4)
I believe the answer is:
awry
'wrong' is the definition.
(synonyms)
'right in a wrong way?' is the wordplay.
'right' becomes 'r' (common abbreviation).
'in' means one lot of letters goes inside another.
'a wrong' is an anagram indicator.
'way' is an anagram of 'awy'.
'r' inserted inside 'awy' is 'AWRY'.
(Other definitions for awry that I've seen before include "Amiss - distorted" , "Crooked, askew" , "Crooked, twisted to one side" , "turning to one side" , "Not functioning properly" .)