The wire you describe has a dual power source. Normally you fuse at each power source to protect the wire not the device. Fuses to protect the device if it has any would be located on the device itself.
Most charge controllers are located close to the batteries with just a short run of wire so most people just install one fuse. I placed a 40A fuse where the #6 wire from the controller (max 30A output) joins the parallel 1/0 wires to the batteries.
#12 with 20A fuse or #10 with 30A fuse would be fine.