Here is an assortment of large sharks that can be found in New Jersey waters, by no means all of them. These are more likely to be found inshore in coastal waters. Sharks are seldom a danger to divers, they seem to be put off by the noise and bubbles. Nonetheless, all should be treated with caution.
In all my many inlet dives, I have seen a shark once, and that was in inoffensive Smooth Dogfish. I have been told that they are sometimes seen from up on the bridge in Belmar, but even then they would probably be out in mid-channel, and far away from strange noisy bubbling scuba divers. However, one of the most famous shark attacks of all time took place in New Jersey - the 1916 Matawan Creek attacks. See Bull Shark for details.
The only one of these that you are ever likely to encounter in local ocean diving is the relatively inoffensive Sand Tiger, not the similarly named and extremely dangerous Tiger.
More: Sharks - Inshore ...