This is another subject that was covered fairly extensively in the past.

I was and still am a believer that small cell size helps in combating
Varroa, but there are no studies that back up my guess. Instead, the only
formal study that I have seen says cell size has no effect. It was done in
Sweden many years ago. I thought the study was not that rigorous.
But... there are trials being conducted somewhere in the south west with
small cell size. Have heard little since the beginning of the trial, even
though much was made about it, I think in Gleanings.
The supposition is that with smaller cell size, you get earlier emergence
of workers so the mite does not develop- except in drone brood, and even
there less since they also emerge earlier. At least that is the theory.

It may work. So many of these home grown trials start out with lots of
noise, but when they fail, you hear nothing.

Two winters ago I tried over wintering with three deeps and got great
results. Figured I had discovered a great beekeeping truth of our time, and
told several people.
This spring I lost my first hive in years and may lose another. Was it the
three deeps? Maybe. It looks a lot more like a reemergence of tracheal
mites, which I carelessly thought was behind us. But it may have been the
three deeps. We beekeepers do not lightly confess our failures, so maybe I
will just blame it on tracheal.... but then that shows I was a beehaver and
not beekeeper, so I'll just keep my mouth shut and go to two deeps next
winter.

For those unfamiliar with my brand of humor, I will not keep it a secret
but will inform the others of my failure. Just like I just did with you, so
please, be kind.

Bill Truesdell
Bath, ME