This is the police station building shown in a photograph from the U.S. Library of Congress’s “Abdülhamid II Album.” The photograph’s caption states that the police station was recently built near Taksim. Since the photograph dates from between 1880 and 1893, the police station can also be dated to the second half of the 19th century.
The location of the building, which no longer exists, has been roughly marked on the map based on the Firuzağa Mosque and the street visible in the photograph.