motor sputters,like out of gas, then you turn the lights on & it runs fine
 

My 1997 king quad 300 cuts out & sputters like it's out of gas. It always idles great. Then if you turn the lights on while it is cutting out, it will rev & run fine for a couple of minutes. Then it sputters. If you turn it off, for a minute, the whole cycle repeats. It has a new carburetor, fresh gas, new plug & I cleaned the ignition switch.

Not sure why this happens as, in theory, the ignition circuit is completely separate from the battery and charging circuit. However, I have had bikes with overcharging voltage regulators, that won't run right unless you have the lights on, as this cuts the voltage going to the battery. Check the voltage across the battery with the engine running, if it goes over 15v when you rev up, you have a faulty voltage regulator.

Actually did the voltage test again. It was 13.5 volts not running, Then started it & it was 13.7, revved up it was 14.0 volts. Isn't that normal? Then rod it about half mile & is seemed to stall, as soon as I twisted the switch to lights position, it cleared up & ran great for about a mile. Then it started sputtering, coasted to a stop & it idles fine, but won't rev. I shut it off for a few seconds, then started it & it ran fine for another half mile & repeats... All the vacuum lines seem fine.

Your voltage regulator tested as OK, but check the voltage when the engine is spluttering. Only other possibility I can think of is it may get a better earth with the lights on, so check the frame to engine earths.

new switch, same problem
 

I just installed a new ignition switch & it didn't help. The motor starts & will chug, sputter until you turn on the lights! Then it will run fine, rev & go for a while. Then it all repeats. So I loosened coil wires & re-tightened, added a ground strap from the battery to the engine. Didn't help...
Just checked the voltage while it is sputtering, over 17 volts! It runs good when the voltage is less than 15, chugs when voltage is too high. What does that indicate?

Your voltage regulator is toast, buy a new one and fit it.

Merryman is correct overcharging is causing ignition CDI to breakdown an this is causing the sputtering running that you are getting CDI cant handle much over 15 volts and when you turn light on that drops down some of the voltage to burn the light and thats when atv runs good and then your CDI gets hot an misfires an this why runs bad again

Good to see ya Papa!