Clicking Noise With Fridge.

IF the compressor is going bad, say shorted windings in the motor, this will cause the compressor to draw to many amps of electricity. When the compressor draws too much current, the overload will overheat and "CLICK". When you hear that click that is the sound of, your refrigerator isn't going to get cold anymore and you better fix it quick noise. That's why you're here
The clicking noise is very distinct and it will sound like it's coming from under the refrigerator or from the back. You may also hear buzzing. The overload will click when it cools down and lets current through the circuit again. So, click off, click on. But if the component parts are bad or the compressor is bad this cycle will happen again, and again, again, and so on and so forth. Usually about the rate of every minute or so.
Now, there are a few other things that will cause this to overheat and shut off. One is if your condenser coils are covered in pet hair and haven't been cleaned in some time. Lint, dust, hair, who knows what else can be there but you get the point. If those coils are not kept clean, the compressor will run hot. That will cause the overload on the side of the compressor to overheat and "click"-no cool. Unplug the fridge and clean the coils. This may fix the problem if the overload or compressor weren't damaged. You will know right away. If the fridge runs fine after cleaning the coils then you are okay. You will know usually within a few minutes if the something has been damaged. It will still click.
Another thing that can cause the click is an adaptive defrost control board. It contains a relay that sends power to the parts on the side of the compressor. When the defrost board doesn't send full power to the compressor, this causes an increased amp draw to make up for the voltage drop. Increased amp draw equals "CLICK"
One more thing that may cause this clicking sound is the condenser fan not working. The condenser fan is the fan that is next to the compressor. It has a couple jobs. Evaporate the defrost water and keeping the heat off the condenser coils and compressor.