I keep replacing 3 amp fuses on furnace and they keep blowing.Why

You have a short or heavy draw in the low voltage section of the furnace. This is why your fuse keeps blowing. Get a meter and check out all the circuits until you find the problem. This is what a service person would do.

Either a low voltage short or bad circuit board. Remove all of the low voltage wires (be sure to label what goes where) and replace the fuse again,power the furnace up,if it does it again it's most likely in the circuit board. Is this a gas furnace or just an air handler?