I just need to know what is the only other circuit that can be attached to a fridge circuit

A fridge can be on a 20 amp small appliance circuit, or a separate 15 amp circuit for the fridge alone.

You can't have anything else on the circuit with the fridge it has to be on its own 20 amp breaker

Hotwire, what is the reference for your advice?

Most refrigerators operate at 7.5 amps, that is why they are recommended to be on an independent circuit. Normally the alternative choice is to place them on one of the 20 Amp counter top receptacle circuits.

However, the best route is the independent circuit is the best choice.

So, what that means to you, first start by reading the required amperage and installation requirements of the refrigerator.

Then determine the circuit you need.

Also, disregard the advice by Hotwire, unless of course the installation instructions require a 20 amp circuit.

If we said a Clock, would you do it because you can.
What do You want to add?
No matter what Code Allows, It is always good too have on its own circuit, so you don't unknowlingly trip the breaker and loose all your food?