TL;DR: Snapper and its species are kosher and considered parve: schoolmaster; muttonfish or mutton snapper; red snapper; yellowtail snapper; kalikali; opakapaka; onaga.
Although not explicitly mentioned in Leviticus 11 and Deuteronomy 14, snapper fits both the criteria for kosher fish. Leviticus 11 presents two criteria for the water-dwelling, namely that it has fins and scales.
Leviticus 11:9-12 These you may eat, of all that are in the waters. Everything in the waters that has fins and scales, whether in the seas or in the rivers, you may eat. But anything in the seas or the rivers that has not fins and scales, of the swarming creatures in the waters and of the living creatures that are in the waters, is detestable to you. You shall regard them as detestable; you shall not eat any of their flesh, and you shall detest their carcasses. Everything in the waters that has not fins and scales is detestable to you.
Snapper (pictured right) obviously fill both of these criteria. Deuteronomy 14, a parallel passage, reiterates verbatim the criteria:
Deuteronomy 14:9-10 Of all that are in the waters you may eat these: whatever has fins and scales you may eat. And whatever does not have fins and scales you shall not eat; it is unclean for you.
There is little or no debate among sects of Judaism regarding snapper, but further considerations should be noted (below).
The blood of fish is traditionally considered kosher for consumption.  Although consuming blood is explicitly denied in Leviticus 3:17, classical rabbis ruled that blood which remained on the inside of meat was permitted, as well as the blood of fish and locusts.
Leviticus 3:17 It shall be a statute forever throughout your generations, in all your dwelling places, that you eat neither fat nor blood.
Fish is considered parve (from the Yiddish parev, meaning neutral), and therefore can be eaten with dairy. Orthodox Judaism holds the position that fish and meat should not be eaten together to avoid causing a disease. Traditionally tzaarat (leprosy) is resultant of consuming meat and fish together.