Add a rotary axis B on a lathe

Ok then your machine is milling machine with a horizontal spindle and a rotary A axis without a Y axis:
your X is the Z,
your Z is the X,
your C is the A,
and the Y does not exist.
In many CAM software you can define the rotary A as substitute for the missing Y so the tool path for Y is wound around the A axis. I have no experience with Fusion360 so I can't comment on how to do it there but I would expect it be able to do that.
The post processor would be the same as for a regular 4 axis linuxcnc mill.

so you might want to change the title of the post to get more information regarding 4 axis milling in fusion360

Thank you very much for this research track.

I looked in Fusion360 and the rotation part is paying. Too bad because it's for leisure.

are you sure? I can generate 4 Axis tool paths but I never tried to post process cause ma mill only as three axis at the moment

yes we can 5 Axes but the problem is the rotation which is in option

Maybe its old information when I started with fusion 4 Axis did work but not 5. Then they removed the 4 Axis and brought the warp toolpath option, which brings most 2d tool pat’s system to 4 axis.
But I didn’t really look into caus I don’t have a rotary (yet)