The finest thread I have ever played with was a #4-256. the thread was barly visible to the naked eye. It was on a tiny carburetor for setting fuel mixture.
Miniature work is so specialized, though; I've always done fine adjustments with differential
screws , like, 1/4-20 on end A of a rod, 1/4-28 on end B, so turning the threaded rod
pulls/pushes two female-threaded barrel nuts by 1/70 inch per turn. For really
fine work, you could make it 12-24 on one end, and M6x1 on the other,
which gives 435 turns per inch (though, of course, 435 turns will require you
to thread a LONG length of rod...).
The best thing about differential screws is, you get LOTS of quick options if there's a big
drawer of taps and dies available....