I was informed this is the Armenian church of Surp Kevork, which was had been the Armenian Cathedral since 1461, when Sultan Mehmet the Conqueror recognized the Armenian Patriarchate of Istanbul, and served as first Armenian Patriarchy for several years.
Another name is Church of St. George of Samatya.
However, the present church only dates from 1913. In my corresepondents knowledge it was an Greek church before the Armenians. Church was burned and rebuilt twice. There is an Armenian Elementary and High school next to the building.