Could someone clarify or explain to me? : Who was the Seljuk Sultan in Osman’s time?- and if it is Allaedin as they say-…

Could someone clarify or explain to me? : Who was the Seljuk Sultan in Osman’s time?- and if it is Allaedin as they say- it seems to me that Mother Sultana is too young- and Allaedin must be very old since with Ertugrul he was already an elderly man- Thank you😊 😮‍💨