In order to be kosher. fish must have both fins and scales. Fish that have only fins are never kosher. There are four types of scales: ganoid, clenoid, cycloid, and placoid. Of these, only cycloid and clenoid scales are kosher in the Torah. Gandoid scales are found on fish like sturgeon and placoid scales are like little teeth (and are found on sharks). Eating fish blood is not prohibited (although other people might think you are eating prohibited blood, which is a different problem). No ritual slaughter is required for fish.
Fish must have true scales, which can be removed without tearing the fish’s skin. As the Torah states – “These you may eat of the fishes, all that have fins and scales…” (Vayikra XI:9-12) Thorn or plate-like scales or bony tubercles that can only be removed by taking off part of the skin aren’t considered kosher scales in this context. Examples of non-kosher fish with these types of scales include: shark, eels, lumpfish, sturgeon, and swordfish. All mammals (such as whales, and dolphins) and shellfish are not kosher. You can only eat the eggs of kosher fish, including caviar or fish roe, but they need supervision.
Be careful when you buy fresh fish if it is filleted, frozen, or even whole, because there is a possibility of substitution with non-kosher fish. It could also be contaminated with remains of non-kosher fish from unclean knives or cutting boards. Buying fish sticks poses three issues: the oil, the fish, and the frying pans and equipment (most of which is normally used for both non-kosher and kosher fish).
To make smoked fish it is usually soaked in brine before being smoked. Often it smoked together with non-kosher fish. In Jewish law, both soaking and smoking are considered the same as cooking over a flame. Therefore, such products are not considered kosher. Also, smoked fish is frequently packed in oil, and this oil may not be kosher.
Herring may be a famous Jewish food, but unfortunately it is not guaranteed to be kosher. The way herring is prepared poses a lot of problems, such as mono- and di-glycerides, bread crumbs, sour cream, spices, non-kosher wine or wine vinegar, and contaminated equipment.
Here is a good list of Kosher and Non-Kosher Fish: