I assume that by deepest you mean below sea level. If so, the deepest volcanoes would be seamounts. Seamounts have received little attention in the past because they are not readily observable. Recent advances in technology, such as side-scan sonar, have greatly increased our knowledge about this type of volcano. They vary in size and shape with most being a few hundred meters tall and circular in plan view.
Most seamounts form along fracture zones and ocean ridges.
Some seamounts are associated with hot spots. If you were thinking something different send me another message.