Yes you can stop mosquitoes using a fan.
Mosquitoes will stay away from you when you have a fan blowing on you because the mosquitoes will not be able to fly in the wind that the fan creates.
The wind from the fan is too powerful for the mosquitoes to fly into so they will avoid the fan and if they do fly around you the fan will blow them away.
This is how I keep mosquitoes away from me when I'm out on my back porch and want to enjoy the outdoors while mosquitoes are out.
I have a couple fans blowing around on the porch with one pointing at me and another pointing to where the mosquitoes are usually coming from.
After using a fan to keep mosquitoes away I still see the mosquitoes but they never land on me.