The tissue should suck up & stick to the grill. If it doesn't, then remove the grill or cover to see if the plug's cord isn't secured & caught the fan blade &/or spin the fan manually. Then, go down & turn the switch on again to confirm the fan actually spins.
Don't put the grill or cover back on yet, I'm not nearly done.
If the tissue does stick nicely then you'll need to check the actual vent path as thoroughly as you can. Go back to the fan & remove the plug & screw that holds the fan in place. You should see a large hole with a plastic flap & the flap should swing open freely.
Your choice here, you can remove the screws that hold the fan-box up & into the ceiling or you can go up into the attic. Take the box down, remembering or marking its position on the ceiling, & remove the fan-box from the vent hose or duct to visually inspect for a clog of some sort.
If no clog then get a much taller ladder, if you've been standing on the toilet all this time, & get a vacuum with a long hose. Leave the vacuum off & feed the hose as far as it will easily go into the duct. If you meet resistance, then turn on the vacuum & slowly pull out the hose, trying to feel if you caught something at that point & can pull it all of the way out.
If nothing at all & you're like 5-feet into the duct, then you'll have to do this further up in the attic. Compress the duct to get your vacuum hose out to the outside vent head or at least closer to it & suck-up any blockages.
If you still couldn't reach the outside vent head, then get a long pipe to tape to the vacuum & get to that vent head. If all's clear & especially was clear the whole time, then you'll have to check, clear or replace the vent head outside & you might as well get a new fan for the bath after all of this effort.