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Fish which has (fins and) even one "kosher" scale is kosher. A "kosher" scale is one which can be removed without damaging the flesh of the skin. In contrast, those scales which are so embedded that flesh is damaged when they are pulled out are not suitable to identify a kosher fish. Some examples of non-kosher fish are catfish, crabs, eels, monk fish, puffers, shark, shellfish, sturgeon, and swordfish.
As a rule, one may not rely on the name of the fish to determine that it is kosher as (a) in some cases multiple fish are referred to by the same name, and (b) there is considerable fraud in the fish industry, with one fish being advertised as another. Therefore, the only reliable method of determining that a fish is from a kosher species is by inspecting its scales, as noted above. One notable exception is salmon, where the flesh-color is unique and is considered a clear identifying mark of the kosher, salmon, fish.
Fish eggs, a.k.a., roe, are only kosher if they come from a kosher species of fish. Since many types of roe look similar, roe should only be purchased with kosher certification.
There are two issues when purchasing cut raw fish - including fillets, steaks, or other cuts - whether fresh or frozen:
Firstly, one must be sure the fish is, in fact, a kosher species, as noted above. If the fish has been scaled, there is no way to determine that it is kosher unless they producer left on a "skin tag"; that tag must have at least one visible "kosher" scale which can be removed without ripping flesh, as noted above.
Secondly, the knives used to scale, eviscerate, fillet and/or cut the fish may have been previously used for non-kosher fish. If that were the case, it is possible that some residue of the non-kosher fish is still on the knife and will transfer to the kosher fish.
The second issue is relevant when purchasing cut fish in a supermarket or fish store. [It does not apply when purchasing fish prepared in an industrial factory, where they cut many of the same fish one after another and there is no meaningful concern of non-kosher residue.] If a kosher fish store is not available, the next best choice is to ask the store employees to clean the knife and work on a clean piece of butcher paper. If even that is not possible, then put the fish under running water and scrub clean, using a brush or by hand, any surfaces that had been cut.
The above only applies to raw fish. Fish which is cooked, smoked, or otherwise processed requires proper kosher certification.