Fuses/circuit breakers protect wire.
If you're fusing at 15A, then all the wire downstream needs to be able to handle 15A.
In the real world, 20AWG will survive 15A indefinitely, but it's not 'best practice' because it'll likely get pretty warm & might stress any insulation shy of Tefzel.
https://www.powerstream.com/wire-fusing-currents.htm
('Fusing current' is the current required to melt the wire.)
If you're saying that you will wire from the 15A protection to a terminal strip with a 14AWG wire, and then split 3 ways to loads, then you could use a small ATO fuse block at that point instead of a terminal block and fuse each branch there.
To be repetitive, circuit fuses or circuit breakers protect wire; not devices.
Charlie