What is the name of the submerged fringe of a continent?

The submerged fringe of a continent is called the continental shelf.

A continental shelf is the gently sloping, underwater edge of a continent. It extends from the shoreline toward the open ocean until the seafloor drops more sharply at the continental slope. Although it lies beneath seawater, the shelf is geologically part of the continent rather than the deep ocean basin.

Continental shelves are generally covered by relatively shallow water and receive sediments carried from land by rivers, wind, and coastal currents. During ice ages, global sea levels fell because more water was locked in glaciers, exposing many shelves as dry land. When the ice melted, the shelves were flooded again.

The continental shelf should not be confused with the continental slope, which is the steeper zone beyond the shelf, or the continental rise, where sediments accumulate farther offshore. The term also has a legal meaning under the United Nations Convention on the Law of the Sea, relating to coastal states’ seabed rights.