In an N-channel MOSFET the current normally flows from Drain to Source. The MOSFET controls the current, depending on the Gate voltage.
MOSFETS contain a diode, so they will conduct in reverse whatever the gate voltage, generally with a voltage drop of about 0.6 V. However, the MOSFET will conduct in reverse if the Gate voltage is raised and then the voltage drop in reverse may be less than 0.6 V.
The current normally flows from Source to Drain in a P-channel MOSFET.