Unjustifiably claimed an idiot's wrong — answers finally will get stuck in (3-6)
I believe the answer is:
soi-disant
'unjustifiably claimed' is the definition.
(soi-disant can mean self-styled or self-proclaimed)
'an idiot's wrong answers finally will get stuck in' is the wordplay.
'wrong' indicates anagramming the letters.
'finally' says to take the final letters.
'will get stuck in' means one lot of letters goes inside another.
The final letter of 'answers' is 's'.
'an'+'idiots'='anidiots'
'anidiots' anagrammed gives 'soidiant'.
'soidiant' placed around 's' is 'SOI-DISANT'.
(Another definition for soi-disant that I've seen is " Self-styled".)