The real history of Baycu Noyan (Baiju) - Mongol Commander appeared in Dirilis Ertugrul Season
Ogedei Khan appointed a Mongolian commander in Persia, who succeeded Chormagan (Mongol Commander and a member of Keshik) between 1230-1260, to extend the Mongol Empire. The commander is called Bayuc Noyan (now an Iranian).
In 1241 or 1242 Baiju came to power and invaded Rome in the battle of Kose Dag (Seljuks Sultanate). He crushed Seljuks during this battle.
The Dirillis Ertugrul Season also featured Baycu Noyan, and his girlfriend, Alangoya or Almila, in which Baris Bagci plays the character of his girlfriend, Baycu Noyan and Gonul Nagiyeva.
Battle of Kose Dag
The Mongol army of the Battle of Kose Dag was commanded by Baiju in the winters of 1242-1243 CE, in which they invaded Rome and put Erzurum in the siege. The Seljuk Sultan Kaykhusraw II, therefore, requested help from the neighboring countries.
Trebizond, therefore, sent a force while Sultan made a group of "French" mercenaries which included some Georgian nobles like Akhaltsikhe's Pharadevla and Shervashidze's Dardin. Despite this, most Georgians had to fight on the side of the Mongols.
The battle in the field of Kose Dag began on 26th June 1243 CE. There's no certainty of precise figures, but Seljuks were big compared to Mongols.
After seeing the enormous hosts of Seldhuk but the commanding officer of Mongols, his Georgian officer was afraid that his troops would not fear the massive army of Seldhuk by saying that it is our pride to defeat many troops.
Kaykhusrav II attacked the Mongols with an army of 20,000 men without waiting for an assault by the Mongols. But the Mongolian army withdrew and overthrew them.
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The Seljuk representatives, the commanders, and some soldiers ran away from the fighting field after their defeat in the battlefield of Kaykhushrav II. Sivas and Kayseri of Seljuks were occupied by Mongols.
He fled to Antalya, Kaykhusrav II. In order to settle peace with them, he had to pay a tariff to Commander Baiju of Mongolia.