I tried 'create cut: extrude' option, but could only model the hole that extrudes through the whole thickness of the plate. But I want the hole extruding only through a depth less than the thickness of the plate.
This sounds like a three-dimensional problem rather than a shell problem. If you were doing it with shells then you would need to specify both a reduced thickness and an offset for the neutral plane. And you would have some fun interpreting the results from such a model.