I have a 96 fourtrax 300 and anytime the battery is connected it continues to turn over even if the key is off. I have had the starter and cilinoid checked and they are fine advice anyone??

 

If you're sure the solenoid is ok,then next step I'd check is the ignition switch for wire harness shorts or a bad switch itself. Still sounds like something a faulty solenoid or relay would do or possibly even the left control switch.1996 Honda TRX300 A HANDLE SWITCH / CABLES | Cheap Cycle Parts

 

Whoever checked the solenoid didn't know what they were doing. The only way a bike can turn the starter with ignition off is for the solenoid to be stuck in the on position. If it were the start button it would switch off with the ignition switch. I have known bikes with an almost flat battery do this. I recon the solenoid moves slower and the contacts arc together.