@Anonymous,
Thanks for posting this issue. I just did a little investigation into the ability to fillet edges after a twisted sweep, and here's what I found.
If you use a straight line or an arc as your path, you should be able to fillet any edges just fine. However, if you try and fillet just the side edges of a twisted sweep where the path is a spline, the fillet is too complicated and Fusion cannot solve it. See the below images for a quick walkthrough of what I mean:

These are the paths I used

These are the results from the sweeps

These are the results from filleting the side edges. Note the one with a spline errors out
However, I did find that if you select all 12 edges in this spline path case, you are able to fillet the entire body. This isn't ideal, but it allows for certain work-arounds like filleting all the edges and then splitting the body where you'd like. See the below images for another demonstration:

The result from filleting all the edges

Creating an offset plane from both ends

Splitting the body
I don't want to launch too deep into the root causes for this limitation, but I just checked the behavior in Inventor, and Inventor cannot perform the same fillet either. This means that the limitation is not in the sweep functionality, but instead in the fillet code in our ASM solver (ASM is the solver that creates the geometry for both Inventor and Fusion). I know this isn't perfect, but hopefully you'll be able to use lines and arcs as your paths for your twisted sweeps, and if that doesn't work, I'm sure you can get creative with extending your paths and then trimming the unwanted portions of the sweeps.
Let me know if you have any other questions!
Lucas Prokopiak
Fusion 360 Product Manager (Sketch/Model)