This is situated near the Kilise Sokak (Church Street), no further information. It looks like a Byzantine church that somehow got destroyed.

I was informed (slightly wrong, but helping me on): These are the remains of the catholikon (main church) of the Studion Monastery one of the earliest and most important monasteries of the Byzantine world. It was dedicated to St. John the Baptist and I think is from the 5th c. It was transformed to a mosque-Imrahor Jami- destroyed by fire.

As a result I could look up in Strolling through Istanbul (Redhouse): "This is the church of St. John the Baptist of Studius, known in Turkish as Imrahor Camii. It was founded by a Roman named Studius in 462 and is thus the oldest surviving church in the city. [...] Nothing now remains of the monastery of the church, the Studion, once the most famous and powerful institution of its kind in the Byzantine Empire. [...] The Emperor Isaac Comnenus, who had studied there as a youth, referred to it as "that glorious and illustrious school if virtue. [...] What was left of the monastery was utterly destroyed in the earthquake of 1894 and now not a trace remians."