At Tiyatro Sokak (nr. 25 or thereabouts) are the remains of what must have been some church.

I found a study, "İznik sarayı çevresindeki kiliseler" by Ü. Melda Ermiş. Having contacted her I can now add: the church has been given the name "The church near Yenişehir Gate." For more information see Semavi Eyice, “Die Byzantinisce Kirche in der Nähe des Yenişehir-Tores zu İznik (Nikaia) (Kirche C)”, Materialia Turcica, Byzantino-Altaica: Festschrift für Hans-Wilhelm Haussig zum 65.Geburtstag, 7/8, 1983, s.152-166.