What does this do? It's located next to the overhead panel of an A320 cockpit.
It's a secret and Airbus does not want you to know.)
Here is the cockpit general arrangement view from the Airbus Flightdeck and Systems briefing for Pilots which labels the visor and rope storage compartment, but the pdf in every version that I looked at only showed descriptions for controls but the graphic did not render. Anywhere.
Next I looked at a flight crew operating manual, where the control is not even pictured but everything around it is. This may be only useful in determining what it is not.
I looked at photos including this one from a German Wings A320 where there are two, so it cannot be that critical a control if this has two, your photo has one, some apparently have none, and nowhere is it documented.
The best answer that I found comes from the cabin crew operators manual which shows ventilation ducts going right through that area on both sides of the overhead panel, terminating in a plenum above each of the pilot and copilot windscreens and showing airflow from those plenums across the windscreens. Since the control is a variable +/- from your picture, it stands to reason that it is a simple airflow control for defogging the windscreen.