Did Ertugrul Ghazi defeat the Mongols?

No, Ertugrul Ghazi did not engage in the Battle of Ain Jalut against the Mongol forces.

This battle occurred in 1260 CE, while Ertugrul Ghazi lived in the 13th century, a number of decades before this event. Known as a formidable warrior, Ertugrul Ghazi was also the father of Osman I, the founder of the Ottoman Empire.