Family man a Corleone? (7)

I believe the answer is:

mobster

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'family man' is the definition.
(I've seen this before)

I cannot understand how the rest of the clue works.

(Other definitions for mobster that I've seen before include "Mafioso" , "Gangster" , "Hood" , "Criminal gang member" , "Organised criminal" .)

I've seen this clue in The Sun.

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