Installing fixture with no junction box and off-center stud
Use a side-mount box and a spacer block
I'd use a side-mount or &quot;L-shaped&quot; type box attached to a spacer block screwed to the stud to handle this -- it'll require some drywall work, but will allow you to attach the fixture solidly to the stud while positioning it where you want it.  (Image below is an Arlington FB442 -- other manufacturers make products that'll work for this as well, I'm sure.)