This is a small Byzantine church converted into a mosque known as Atik Mustafa Paşa Camii. Strolling through Istanbul, a great guidebook, tells us it was until recently (I quote from my 1989 edition) identified as the Church of SS. Peter and Mark; a designation that now is generally abandoned, without a convincing alternative. It seems to be a 9th century church of which the Gül Camii and Kalenderhane Camii are earlier and grander examples. The wooden porch, dome and drum are seen as Turkish restorations. For the rest the church preserves its original plan which is simple and, for a Byzantine structure, regular. A dome, “doubtless originally on a fairly high drum with windows, covers the centre of the cross; the arms are barrel-vaulted, as are the four small rooms beyond the dome piers which fill up the corners of the cross; they are entered through high, narrow arches. The three apses, semicircular within, have three faces on the exterior. It must have been an attractive little church and it still has a decayed charm”.
From the Wikipedia I understand the mosque is also named “Cabir Mosque”, there the claim is made it is from the 121-12th century. Inside is a türbe (tomb), which the Wikipedia names the “The alleged türbe (tomb) of Hazreti Cabir (Jabir) in the south apse.” Elsewhere in the article a full name is given: Hazreti Cabir (Jabir) Ibn Abdallah-ül-Ensamı, one of the companions of Eyüp.

I came across a site with reconstructions of Istanbul monuments around 1200, for instance the Atik Mustafa mosque.