Translated from a Turkish website: "The founder of the mosque is Mehmet Ağa, the armorer of Fatih Sultan Mehmet. While he was called "Küçücük" because he was small, the name began to be called Köçek as a distortion. He is from Nimelceyş. The mosque underwent extensive restoration in the 19th century and lost its original appearance."
In 2024 I was struck by the form of the (top of) its minaret and decided to pay it a visit.