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' (abbreviation).
'in' indicates putting letters inside.
'a wrong' indicates an anagram.
'way' is an anagram of 'awy'.
'r' placed into '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" .)