What amperage fan is safe to replace my 0.13A fan?
Because your fridge uses a 12V fan, I'm assuming that it uses a thermo-electric cooler (Peltier cells) rather than a compressor like a larger fridge would use?

If so, the actual fan current is probably of no consequence.  The thermo-electric cooler requires significant current at 12V and the power supply most likely wouldn't know about or care if your replacement fan consumes more or less current than the original.

Suggestion: look for the quietest fan you can find.  Don't worry about how much current it consumes - just make sure that it runs from 12V.

I've recently had to replace the fans (both in power supply and on top of CPU) in a couple of professional hard-disk of multi-track audio recorder decks and it is absolutely amazing how quiet some of the new fans can be while still moving significant amounts of air.  There was nothing wrong with the stock fans other than that they were far too noisy to be used in the control room where they were situated.  The new fans were chosen to have at least the same amount of CFM as the originals but with significantly less noise.  The difference was impressive.