In which region MOSFET works as an amplifier and in which region MOSFET works as a switch? Does MOSFET work as a switch in the saturation region?

 

A MOSFET can work in the linear region for a class AB amp or in switching mode for a class D amplifier.

 

Generally if you need a transistor in the linear region you use a BJT, not a MOSFET. A BJT has a wider range that is truly linear, while a MOSFET is a really good switch, with a incredibly low conductance when it is on (well under 0.1Ω typically).

If you must use a MOSFET in its linear region then be aware you are throwing away most of the advantages of a MOSFET. It will get hot, but that is true of a BJT also.

There are logic level MOSFETs designed to work with lower voltages, but generally a conventional MOSFET requires 10V or more on the gate to turn fully on. Less than that can (not will) put it in it's linear region.