Give a wrong idea of felon's first conviction (6)
I believe the answer is:
belief
'conviction' is the definition.
(I've seen this in another clue)
'give a wrong idea of felon's first' is the wordplay.
'give' says to put letters next to each other.
'a wrong idea of' becomes 'belie' (I can't justify this - if you can you should give a lot more credence to this answer).
'felon's first' becomes 'f' (bst letter of 'felon').
'belie'+'f' is 'BELIEF'.
Can you help me to learn more?
(Other definitions for belief that I've seen before include "Conviction, faith" , "Persuasion" , "Creed or opinion" , "Credo" , "Tenet, creed" .)