The Sahib Ata Vakıf Müzesi is part of the külliye of the Sahib Ata Camii. It dates from the heyday of the Seljuk (1259). I did not enter the mosque, but I took pictures of the monumental entrance gate to the mosque, and then went and saw the beautiful museum. It houses a number of wonderfully restored türbes of the founder and his family, as well as a few kürsü, prayer chairs, that are ancient, and several other small artifacts, like a number of good kilims. The central hall is magnificent, and I strongly advice a visit to this museum. It has the advantage of being very close to the archaeological museum, which is a treat in itself.
Sahib Ata was for 50 years one of the leaders of the sultanate of the Rum Seljuk, until he was beheaded by the Mongols in 1277. He founded many major buildings in the Sultanate, amongst them in Konya the Ince Minare Medrese and the famous Gök Medrese in Sivas.