The mosque is the Ayazma Mosque, built 1760 by Sultan Mustafa III and dedicated to his mother. It is in a baroque style, and has some great ornaments that I did not hesitate to take pictures of. Also, it has several "houses" on its walls, meant for pigeons.
I have been informed by the book Ottoman Baroque (Ünver Rüstem) that we here see a mixture of older style-elements and baroque ones, i.e. stepped outlines of the baldachin and the windows in the façade of the mosque, which have an arch of the four-centered type, versus pilasters carrying Baroque pinnacles with finials in the shape of crescent moons.