The Yuan Government put practice the system of Four Classes very strictly. They divided their citizens into four classes. The first class is Mongolians. The lowest class is the Han living in South China. You can read the page for the details of the System of Four Classes:
https://www.travelchinaguide.com/intro/history/yuan/four-class-system.htm

In the Yuan Dynasty, the conflicts of society mainly include the conflicts between ruling classes and ruled classes and the conflicts of ethnic discrimination.