To be precise: this is not a mosque, but a medrese (Kuran school) that is part of the mosque complex.

The complex was built in 1460, commissioned by Sitti Hatun, a daughter of Oruç Bey, the second son of Kara Timurtaş Paşa. The latter was grandson of Aygut Alp (a famous comrade of Osman Gazi, the namesake of the Ottoman dynasty) and was appointed ‘beylerbeyi’ (governor) by Murat I. His son Oruç Bey was the first known court historian of the Ottomans; his daughter Sitti Hatun became the first wife of Zağanos Mehmed Paşa, a life-long companion of Fatih Sultan Mehmet II, with an impressive career as tutor, army commander, Grand Vizier and Governor. No wonder his wife had some money to spend on community service.

The medrese (or rather: ‘Mektep’ = school) lies to the East of the Sitti Hatun Mosque. It is also referred to as ‘Kamberler Mektebi’ (School of the Kamberler neighbourhood). It has been restored several times, last in 1962.
It is the nicest and best preserved example of a 15th century Ottoman ‘mektep’ in Bursa. The building has a rectangular shape (12,5 x 6,7 m) and is divided into two domed classrooms of 5 x 5 m; the first room (on the West side) has the form of an ‘iwan’, opening onto the exterior.

An iwan (Persian & Turkish: ‘eyvān’) is a rectangular hall or space, usually vaulted, walled on three sides, with one end entirely open. This architectural form can be used for entrances, but also to create half open rooms looking out at a central yard (which was the case in Seljuk medreses).

Correspondent: J.M.Criel, Antwerpen.
Sources: ‘Vakıf Abideler ve eski Eserler (volume III)’ - Vakıflar Genel Müdürlüğü, Ankara 1983 & Wikipedia.