No, a 20A fuse will be too small. I can get 20A peak out of a 36V 4AH battery powering a 250W motor. It's the controller, in my case a 20A controller, that controls current flow.
Look at your controller label and see if it says max current. That will give you fuse info. Most people don't use fuses. It adds complexity, and if the fuse is poorly installed/wired in, it will get hot and waste power if that happens.
The amp hour rating of a battery is a rating of its capacity. 20AH is capable of 20A for 1 hour, 10A for 2 hours, 2A for 10 hours, etc. You would have to know how the battery is actually made to know its max current potential. For example, A 20AH lead acid battery is different from a 20AH lithium battery. And for lithium batteries, you have to look at the number of cells in parallel, and their brand.