I've been using a 40Mm sunon Maglev fan in my 1.8 cubic foot 12v compressor fridge. It draws only 0.03amps, moves only 6.3cfm
It greatly speeds cooling of warm items placed within, and evens out internal temps all to within 1.5 degrees of each other, whereas without there can be a 15 degree spread from warmest spot to coolest.
With such a low amp draw, I just let it run 24/7, and in October this year, it will be running continuously for 4 years. I took power for it from the LED light.
The fan motor generates some degree of heat which then must be removed, so overall the fan can't help the fridge use less power, but I have power to spare. When I put warm beer inside of it I want it cold ASAP, and this internal fan makes a huge difference in the time it takes to make warm cheap american beer drinkable.
Absorption fridges cool so much slower I've no idea how well internal fans would work in them, but I certainly would not buy fan marketed for a fridge, but search out a low CFM low amp draw dual ball bearing computer fan or a hydrodynamic bearing fan and make my own mounting method.
These fans can vary extremely widely in amp draw for air moved and noise made.
Not much CFM is needed for inside the fridge and the slower and lower the amp draw, the less heat will be introduced into the fridge.