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It might be a Red Mouthed Goby or it could be goby with a red mouth, several features are required to 'nail it down' the red mouth is one, it should also have small 'free' fins at the front of the pectoral fin like the rock goby has,
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yours could have them or not depending on how you interpret the photo
but even if it does it could be a reddish rock goby. a species that also has a light coloured fringe to the dorsal fin.
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The British Marine Life Study Society group would be interested to know the area of capture as it would be a new place as they are only recorded in Southern Ireland.
My opinion is that it's a 'maybe'
If it is it is a rare catch and a matter of scientific interest.