I have a 38 inch cut murrary rideing mower and it dies after about 15 to 20 min. of use. It will start right up but dies again in just a few min. while mowing and its harder to start up you have to let it sit for a few then it will start right back up again. I figured it might be the carb but I'm not for sure.

I also wanted to add it has a 12.5 hp motor and the model number on the motor is 21A707-0223-E1. And some other number 030926za

What brand engine, B&S?

Yes it's a briggs. 2003 model I think.

I would start by testing the coil. Have a spark plug wrench ready and run the mower until it dies. Pull the plug and reattach the wire. Allow the plg to be grounded againist the block and try your starter. You should see a bright blue spark at the plug, if not your coil may be heating up and failing.