Have12.5hp rider after 10 min motor will die.when it cools off it will start again. Whats wrong

You have a valve problem they are getting superheated and unseating them selfs when there hot and makes it hard syarting need valve job done

Sounds like its a fuel starvation problem, an engine will generally run fo approx 10 mins with a bowl full of fuel before stopping. check that the fuel is running out of the pipe at a good steady rate. if not the fuel tank,pipe or filter could be blocked. if fuel is flowing ok then the carb will probably need removing and cleaning, but you may get away with just removing the carb bowl and cleaning it out

Change the spark plug
if no better suspect the coil

Check the fuel cap vent is not blocked this will draw a vacuum in the fuel tank and prevent the fuel flowing after a short time.