Is there a mini ceiling fan that I could screw into a ceiling light fixture socket?
Maybe with a bulb, too?
Links help.
This sort of thing ?
ETA: I notice that site doesn’t have it available. If I’m on the right track, I can poke around a bit 
There used to be one called the BreezeLite, but it was discontinued. I can’t find any similar things available today, although someone somewhere probably does make one.
I have my suspicions about why the BreezeLite was discontinued. A socket isn’t going to support a fan of any size to actually get much air circulation. And depending on the direction of fan rotation, I’d think it would either quickly unscrew itself or tighten itself enough that you couldn’t remove it easily.
Replacing a fixture is pretty easy and is the route I’d take.
ETA: this is the same one linked above. It’s unavailable anywhere, not just on QVC. The company is gone.
Yeah!
A new fixture is too much trouble to air out a closet.
I think it was what you’re looking for, but I don’t see any availability:
Maybe try eBay ?
Maybe use one of those desk clip on fans, if you just need to get air circulating?
Something like this?
If there’s no outlet, you can get one that screws into the light socket. They make pass-through ones where you can still have a bulb in, or converter ones that are just an outlet.
Maybe too complicated or too jury rigged for your needs?
Had something like that, & it was a pain.
This is the way my dad did it:
E27 To Double E27 Base Socket Extender Adapter Converter LED Light Lamp Bulb | eBay
Lamp Screw Base Bulb E27 Bulb To US/EU Plug Adapter Light Holder Socket Converte | eBay
Yeah, I had something similar–caused issues.
Maybe what you need is an air purifier https://www.amazon.com/Purifiers-Home-Dehumidifier-Portable-Purifier/dp/B08NK141H4/ref=sr_1_5?dchild=1&keywords=closet+air+purifier&qid=1615602539&sr=8-5