Hi
As you know, running a stepper motor is more than a little problem: coding and driving. This project is more sophisticated when you want to build a stand-alone device . The powering is one the major problems.
I've made a syringe pump, with UNO, A4899 and a stepper motor ( and a lot of button, LCD, multi-turn). To best of my knowledge, maximum 1 A will cross per winding. I'm thinking to use one or two fuses. I think, it's not necessary to use a fuse for UNO, because i'm using a wall adaptor. But what about the A4988? Vmot is from the wall adaptor too.
The usual purpose of a fuse is to prevent the wiring from overheating and starting a fire in the event of short circuit. And fuses are normally selected to trip at a current (amps) that is significantly higher than the normal operating current. Otherwise you would get fuse failures during normal operation.
I would not consider it necessary to have a fuse downstream of a plug-in mains power adapter unless, for some reason you have an adapter that can provide a very high current and you are using cables that cannot handle that current. However it would be good practice to choose a power supply that can provide at least 50% more current that your system requires. It is not a good idea to operate electronic equipment close to its limit.
You should adjust the current limit on the A4988 to match whatever current is permitted by your motor.
...R