Soak the codfish overnight in cold water. Drain in the morning and soak for 1 hour in cold water. Drain.
Put the fish and raw potatoes in a sauce pan, cover with water, and cook until the potatoes are tender. Drain off the water.
Beat the egg and blend in butter. Add the pepper and dry mustard. Add fish and potato mixture, beat well.
Drop by tablespoonsful into hot fat and fry, turning to brown all over, until a rich golden brown.