Etymology

Butter bei die Fische, literally: “butter with the fish” (plural). The same in Dutch boter bij de vis (with a similar, but not entirely identical meaning).

The idiom is grammatically peculiar because it uses the accusative case (die Fische) with the preposition bei, which is incorrect by contemporary standard rules. The phrase is from a German Low German source. In many German dialects, including Low German, bei can express location (with dative) but also movement (with accusative). Compare other German prepositions varying between dative and accusative in the same way, e.g. in, auf, etc.