Who was Ertugrul the son of Suleyman Shah.
1. The trustworthy scholar of Damascus, Qadhi and Historian Shaykh Ahmad bin Yusuf Qarmani (d 1019 h).
In his book اخبار الدول و آثار الاول فی التاریخ: ج 3، ص 6،7 he mentioned Suleman Shah that how he along with Sultan Ala ud din fought Mongols and other disbelievers and after his death his son Ertugrul did same thing i.e. alignment with Sultan Ala ud din and did Jihad with disbelievers and won various places until he died fighting them. When Ala ud din came to know about his death he did condolence and gave his son Uthman his place.
2. The Egyptian Historian Muhammad bin Muhammad bin abi al Suroor al Bakri (1060 h)
In his book منح الرحامنیة فی الدولة العثمانیة mentioned Suleman Shah had four sons, two went to Ajam and two came to Sultan Ala ud din and lived in his land after his consent and did jihad with kuffar and died while fighting them.
3. The Tunisian historian Ḥusayn Khūjah (d 1145 h).
He mentioned same in his book بشائر اهل الايمان بفتوحات ال عثمان
Special Thanks to Brother Muhammad Shahrukh Khan who provided Scans and references, this post is translated from his wall.