How to keep gnats out our refrigerator?

Probably fruit flies - The fruit flies have laid eggs somewhere in your fridge. If there are any drain traps or any extra covers for electric/whatever take them off. Spray the entire fridge with a spray cleaner that has bleach. Then unplug fridge and let it dry out.

Fruit flies get in when you open the door. If you store fruit in there.....that is what they are attracted to. They hitchhike home on fruit you buy so wash fruit thoroughly as soon as you get it home. Try storing it in plastic containers in the fridge.

I have no idea who has the time to empty their entire fridge and let it dry out. I don't want any bleach in my refrigerator anyway.

Removing all items periodically from the inside of the fridge and giving it a thorough cleaning is sensible home management. It prevents food gunk and sticky buildup and helps to keep the inside of the fridge fresh smelling. It really does not take that long a time to do this.

To speed up drying, especially if you live somewhere with high humidity, aim an electric fan towards the inside of the fridge with the door open.

You bring them home in your produce. Head lettuce is great for hitch hiking gants.