The most common method to remove rusted faucet screw is using a drill. A power drill makes installing and removing screws so much easier and faster.
To remove the stripped screw, select a drill bit that has a diameter big enough to fit into the slot of the screw. Position the drill on the screw and start drilling till you reach the center bottom of the head.
Doing this will make more space to create more friction when you want to drill out the screw next.
Now change the drill bit into a bigger one that has the same diameter as the screw-head. Insert the bit into the hole you created earlier and start the drill in the reverse direction.
Since the new bit is bigger, it will create more friction with the screw and thus loosen it. In this step, don’t drill anticlockwise too fast but instead apply a bit of patience by going slow.