How can I lower the speed of a 220-240V (100mA, 16W) inline ventilator fan?
Can you please let us know which mosfet you are using its number, you can control the fan speed using RC circuit also like we have in the fan regulator other cheap way is no need of arduino just use your fan regulator it will do your work and save your money also.
But if you still want to use arduino to control the speed of the fan you can use pwm of the arduino which will give variable output and then you will need a mosfet and mosfet driving circuit which will be connected to the fan and the arduino. You can also use triac and its driving circuit to control the fan speed in replacement of MOSFET