Funny rhyme for a fish (5)

I believe the answer is:

tunny

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'fish' is the definition.
(tunny is a kind of fish)

I don't understand the remainder of the clue.

(Other definitions for tunny that I've seen before include "Warm water food fish" , "A tuna" , "Marine fish, the bluefin" , "Large marine fish" , "Common food fish" .)

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