It was far from unheard of for Turkic groups to come galloping in off the Steppes and overrun large swathes of a region, for a time.
ASB as this requires turks to move from eastern steppes all the way to anatolia. They were nomads, but still..
Happened more than a few times. In fact, they wouldn't have to go far: The Oghuz Turks of Transoxiana and the Aral steppe would be a good bet to pull this off. Quite a few of them operated as mercenaries already and returned home with new religions and connections. OTL, the Oghuz ended up splitting off due to a tax revolt, with the Bayat, Kinik and Kayi clans migrating north of the Caspian and preying on the weak principalities left over from the fragmentation of Rus. Between them and the Pechenegs, the Rus remnants were so battered that they just rolled over by the time the Cumans arrived and settled down, even taking Taurica off the hands of the Greeks.
The Oghuz were apparently quite powerful, especially the Kinik, and even today the Uzes - the descendants of the Oghuz - form a distinct ethnic minority within the Qirim Republic; while most of the cities along the northern Black Sea (the Karadeniz Rim) and on up to Qiyib[1] are ethnically Cuman or Cumanized Slavs, the Uzes tend to live up in the Havasoq Mountains[2] near the border with Hungary, and they tend to be the only Catholics in a mostly Orthodox country, save for the Muslims who mostly came from the Kinik group.[3] That's mainly because the Cumans pushed them there when they arrived, just like the Cumans got compressed into the Black Sea Steppe when the Khitans arrived. They might've been pushed further had the Khitans not swung south around the Caspian to attack Georgia and Persia.
Maybe if some group of Uzes went south after the tax revolt, they could have achieved success against the Persians. At the time, the Persian Resurgence was just on the upswing, with the Buyids controlling the Abbasid Caliph. An arriving Oghuz horde might have been able to stop the Persian Resurgence in its tracks and continue on to attack Anatolia. The region's interior was always sparsely populated, and the arriving Oghuz could win a few lucky victories and settle in.
That timeline would be interesting. I wonder how Islam would look without its co-option and reform by the Persians and the reduction of ethnic Arabs to tributary status. I bet Shiism would be a lot less prevalent.
[1] Kyiv.
[2] The Carpathians.
[3] The Seljuks.