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The correct fuse for the 14 Gauge wire is 15 amps.
You are protecting the wire from causing a fire when selecting the fuse. You select the gauge of the wire for the total load it will see, the fuse is set to protect the wire.
There are also different kinds of fuses like slo-blo to handle short high current loads. If you use a breaker instead of a fuse the size of the breaker may be different then a fuse.
Fuse to wire gauge chart link