Can I buy filleted fish from a local fish store, which is not under rabbinical supervision?
There are two issues we should bear in mind to answer this question 1.Identifying the fish and 2. Using the same knife.
Identifying a kosher specie is a Biblical positive commandment. (Lev. 20:25). Modern rabbis discuss if and when is possible to recognize a fish fillet.
I quote here two opinions on this matter. The first represents the standard Ashkenazi opinion and the second the standard Sephardic opinion.
1) According to the stricter opinion a fish can only be identifiable if it still has some of its skin (=visible scales). Filleted fish with no skin left, cannot be properly identified. Therefore, you cannot buy it from a non Kosher store. This is the rule for whole fish and obviously for fresh or frozen skinless-fish-fillet (See guidelines and exceptions here).
2) According to the Sephardic custom (as per Rabbi Eliyahu Ben Hayim שליט"א for example) if you can recognize this fish fillet as a Kosher specie --for example, if you would be able to identify this fish among five other filleted fish--then it is permitted for you to purchase that fish, even though the fillet does not have any more skin. This is the case for fresh or frozen fillet.
Now, what about the knife? Can you buy a fish that was cut with a non-Kosher knife?
1) Some Rabbinical authorities require to take your own knife to the fish store and use that specific knife to cut the fish, in order to avoid any cross-contamination between the Kosher and non Kosher fish by means of the knife or the cut board (see idem).
2) Rabbi Ben Hayim explains that you can buy a filleted Kosher fish even if the seller uses his own knife, if you do a couple of things. 1. Make sure make sure that the seller washes the knife with water before he cuts the Kosher fish. That will remove any solid vestiges or traces (isur ba'ayin) of non-Kosher fish that might have remained in the knife surface (cross-contamination of taste particles is not relevant when the fish is cold) . 2. Once at home, you must wash the fish with water before cooking it to make sure that no solid vestiges or traces of a non Kosher fish remain in your fish.
(Psalm 120:7) אני שלום וכי אדבר המה למלחמה
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