My riding mower has a Briggs engine Model 28A707, Type 0113 01,
Code 9402124E. After running for about 20 minutes it quits. Then it won't turn over. After a while it will turn over and start, and run for another 20 or so minutes.
The battery is new but it did the same with the old battery.
I suspect the engine is running directly off the battery. It there something in the
Starter, that is supposed to provide the electricity to run the engine, that is
Not working. If so do I need to get a whole new starter?

Hi,
There is a stator beneath the flywheel that charges the battery. There is no way for the machine to run off the battery; however, if it has an electric PTO clutch and an anti-backfire solenoid, the clutch could discharge the battery to the extent the solenoid closes cutting off the fuel supply.
Inspect the wires coming from the engine, generally one white and one red. The red one could have a diode that is bad. You can use a VOM to check battery voltage at the battery with engine at full throttle. It should be between 14 and 16 V.
Peace,
Clarke
Peace,
Clarke