12/2 to 14/2 wire question

I ran a 12/2 out to my garage on a 20 amp breaker for running saws and other larger power drawing tools. I have ran 12/2 wire to a couple 20amp plugs. My question is can I run 14/2 wire off one of the plugs to feed my lights and other 15 amp plugs? If not is there and way I can junction the 12 and 14 wire inside my garage. I am not able to run new 14/2 out to the garage. Also what would the issue be with just connecting the 14 to the 12? Would it melt the wire, start a fire ...??

Thanks Gary