Publication penned by Godfather, monster (6)
I believe the answer is:
dragon
'monster' is the definition.
(I know that dragon is a type of mythical creature)
'publication penned by godfather' is the wordplay.
'publication' becomes 'rag' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'penned by' is an insertion indicator (inserted letters are penned in).
'godfather' becomes 'don' (I've seen this in another clue).
'rag' going within 'don' is 'DRAGON'.
Can you help me to learn more?
(Other definitions for dragon that I've seen before include "Fury" , "Fire-breathing reptile, usually with wings" , "Intractable person" , "Seventeen [HARRIDAN]" , "Fire-breathing creature slain by St George" .)