This Türbe or cenotaph is from 1343, on the notice it says it's the Kutluş Hatun cenotaph. It's directly in front of a complex, that's the Hunat Hatun Külliyesi: the usual complex of mosque, medrese and mausoleum.

According to the building inscription, written on a white marble plate and placed high above the entrance door, this mausoleum was built in 1350 (Eretna Beylik period) by princess Şah Kutlu Hatun for two of her sons: Emir Haydar Bey and Emir Bahşayiş. The style of the Late-Seljuk stone work decoration is a faithfull imitation of the preceding Ilhanlı period. The mausoleum was last restored in 1977 and 1992-93.

The ‘Eretnaoğulları’ was an Anatolian beylik (principality) that succeeded the Ilkhanid governors in Anatolia and that ruled in a large region extending between Kayseri, Sivas and Amasya between 1328–1381. Although short-lived, the Beylik of Eretna left important works of architecture.
The dynasty's founder, Alaeddin Eretna, was a Mongol officer of Uyghur origin in the service of Timurtaş, the Ilkhanid governor of Anatolia. After his master unsuccessfully revolted in 1327, The Persian Ilkhan Abu Said appointed Eretna a governor of Anatolia. When the Ilkhan rule collapsed in 1335, Eretna was able to establish his own beylik with the title of Sultan under the protection of the Mamluk Sultanate (Egypt). After Eretna's death (1352), his lands were nibbled away by the Ottomans in the west and Akkoyunlu in the east due to internal disputes between the Eretnids. The Beylik's last ruler, Muhammad II, was replaced by his vizier Kadı Burhaneddin who reigned in the same region for another eighteen years.

Correspondent: J.M.Criel, Antwerpen.
Sources: ‘Kayseri Kültür Varlıkları Envanteri’ (Kayseri Belediyesi 2008) & Wikipedia