How can I run a 3/14 15amp wire from a 3/12 30 amp wire

Note: Unless specifically permitted, the rule is always: 12AWG should not exceed 20 amps, and 14AWG should not exceed 15 amps.

There is nothing stoping you from mixing gauges, but I highly recommend that if you plan to mix, make sure the wire at the panel identifies the smaller gauge. It wouldn't be wise to have a 12 gauge wire at the panel, then down the circuit you have a 14 wire mixed in-- this may lead someone to believe the entire circuit is 12 wire-->leading them to install a 20amp breaker.

What are you trying to accomplish?