It is very common to reduce the size of the current carrying conductor, whether it be cables or printed circuit board traces, as you progress further from the power source to the loads.
Residential power distribution is a good example of this. Coming into your home you may have a 200 amp service that goes into a breaker panel. This panel is protected by a circuit breaker with a rating of 200 amps or less. That panel then branches off to multiple #14 , #12, or other size cables, protected by 15 A or 20 A breakers (to protect the wiring). At the individual outlets, a device that's plugged in (like a TV set) may have it's own fuse to protect that appliance. That fuse's size (1 A, 2 A, etc) may be much lower than that of the supplied branch circuit.
Here's another example. We have a system with a 200 amp power supply that feeds multiple (several hundred) 1 A loads. The individual loads are designed in such a way that they disconnect themselves from the power in the case that a short develops within them with a fuse-like element. This is to protect the system wiring and allow the system to continue to operate with one or more of these loads removed. There are no discrete fuses as such in this power path, though the power supplies are design with overload protection. One of the trickier parts of this design was ensuring that you had enough current at the faulted load to open the protection mechanism, but not a high enough current that the interconnections would be damaged.
Edit 1 - Added Sketch Below
Without knowing more about your system, it's hard to say definitively what you need. But as a first cut, I would start off by sizing your conductors for a 10 deg C temperature rise or, alternately, the max voltage drop you can tolerate. This means much smaller conductors for the 0.5 A paths than for the 20 A path. Then I would fuse each 0.5 A path with a fuse or breaker with the appropriate time*current trip characteristic. This may turn out to be a 1 A, 2 A, or 5 A fuse or breaker.
