Fight with twin, reportedly (4)
I believe the answer is:
duel
'fight' is the definition.
(I know that duel is a type of fight)
'twin reportedly' is the wordplay.
'twin' becomes 'dual' (I've seen this in another clue).
'reportedly' indicates a 'sounds like' (homophone) clue.
'dual' is a homophone of 'DUEL'.
'with' is the link.
(Other definitions for duel that I've seen before include "Fight between two persons" , "Fight over a point of honour" , "Affair of honour (between two men)" , "Contest between two people, perhaps with weapons" , "battle" .)