Whose bright idea was to stick a light there with all that surrounding wall space. IMO that light in the wrong location and will not do much other than provide some glow for that glass block window. Based on what I can tell from that picture I would rewire and have nice wall sconces on each side of that window.

That said, you would see small backplates on the light fixtures that intended for reading lights near or above the bed, etc most fixtures have standard light plates. Just try to Google "light fixtures with small backplates" and see what comes up.

Good luck

Agree with GN Builders re: rewiring. But, if that is not your choice you should be able to find fixtures with narrow backplates - you just wont have many options to choose from. Try searching for bath bars, narrow or thin line. The fixture from Lamps Plus below has a 2.5” back plate.

Hudson valley lighting makes fixtures with small back plates, and yes picture lights and swing arms can sometimes have them. You have more than just the problem of the 4" look at the space above the box to the ceiling, there is none.

Perhaps your best option would be a custom light made according to your requirements, if you're interested I might be able to help you with this, I make custom fixtures based on the client specifications. Feel free to check some of my fixtures here: RSW STUDIO LIGHTING

PS: Every single one of my fixtures can be customized and can be done with smaller back plates.