XT1 24hp kohler just serviced ran fine turned off now does not turn over

Running for about a minute sounds like fuel starvation. There could be an obstruction in the fuel tank, which allows the engine only the fuel that is in the fuel line, until it quits.
Why it won't start again is probably another matter.

Ron, Try new plug/s first, sounds like the carburetor has dirt in it, you will probably have to remove carb. and clean/rebuild. From manual, other causes from your trouble shooting guide ,
? Faulty carburetor. ? Faulty cylinder head gasket. ? Faulty or misadjusted choke or throttle controls. ? Fuel pump malfunction-vacuum hose clogged or leaking. ? Intake system leak. ? Loose wires or connections that intermittently ground ignition kill circuit. ? Quality of fuel (dirt, water, stale, mixture). ? Restricted fuel tank cap vent. Check the attached links,instruction and guides, Good luck
"I hope this helped you out, if so let me know by pressing the helpful button. Check out some of my other posts if you need more tips and info."
http://www.kohlerengines.com/onlinecatalog/pdf/32_690_03_EN.pdf
Kohler KT735 3013 24 Hp Engine Parts
Kohler carb rebuild
How To Rebuild Kohler Series Carburetor K161 K181 K241 etc

now the kohler v-twin does have a bit of a problem with camshafts in this size range , your gonna need to remove valve cover on head side that you suspect is bad , verify that valves move in order (one at a time) as you turn over by hand with spark plugs removed (both sides)

if that is the Kohler 14 hp motor it may have the spark control untit on the motor cover. I recently ran into one like that and switched the coil out from a blown 20 hp kohler engine. I just taped up the excess wires and made sure they were not near any moving parts. The mower ran fine after that. Kohler wants about $160.00 for a spark control unit. There have been no repercussions since making the switch.

there are some magnets behind the flywheel to cause the battery charging system to recharge the batt. sometimes they come unbonded/loose from the flywheel and cause the engine to become hard to turn. I would start there first.

clean out fuel line then make sure the carb is getting gas

This is the Kohler K321 engine.

You can find the service manual here: (14.16 mb)
http://www.kohlerengines.com/onlinecatalog/pdf/tp_2379.pdf

The inital carb adjustment setting procedures start on page 29
Kohler carb low idle 2 1/2 turns from closed Walbro carb 1 1/2 turn from closed
Kohler carb high idle 3 1/4 turns from closed Walbro carb NA

Thanks for choosing FixYa,
Kelly