According to tradition, it was a haddock in whose mouth St. Peter found the stater (or piece of money), and the two marks on the fish's neck are said to be the impressions of the apostle's finger and thumb. It is a pity that the person who invented this pretty story forgot that salt-water haddocks cannot live in the fresh water of the Lake Gennesaret. (See John Dory and Christian Traditions.)
O superstitious dainty, Peter's fish, How comst thou here to make so goodly dish?
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894