Install Bath Fan 1st floor with parallel joist to exterior wall
I have done several different things here. In several houses I have mounted the fan directly on the wall close to the roof with the exhaust going through the side. 
I have also mounted the fan in the first 16” and punched a 4” hole through the joist is sitting on the wall so it’s not a structural problem.
The 3rd and hardest but best looking was to build a small plenum with intakes mounted horizontally at the top with the exhaust through the wall, I also incorporated some lights in the plenum so it looked very nice.
The fan on the wall direct exit was the easiest but did not look that great to me. I have used this on homes we flipped where cost and speed matter.

With the fan in the ceiling close to the wall it looked ok but it was closer to the wall than I thought looked good I have used this method many times on new construction it can be done in a remodel but drilling through the sheathing and siding is a bit tougher on a remodel but can be done, if pulling some Sheetrock down it is much easier.

In my own home I have the plenum it really looks nice and is the quietest but close to 3x the cost of just a fan and a exterior jack with a damper.  we used this method on ~half a dozen spec homes and I like it the best.