Upvote:2
There were certainly lots of battles in history in Central Anatolia, but it looks like the Byzantines held onto political control of that area up until the Seljuks won the battle of Manzikert(1071) and took almost all of the interior of the peninsula from the Greeks.
The Mongols briefly took control from the Turks in the mid 13th-14th centuries before their Khantate collapsed (probably more due to the Black Death than anything else), at which point the resident Turks reestablished control. Its remained in Turkish hands ever since.
The Abbasid Caliphate did manage to come fairly close, particularly in their early days. Around 830-960ish they had control of Tarsus (on the coast south of Kayseri) and Malataya (on the upper Tigris east of Kayseri), with their border extending roughly in a line between the two.
There were probably numerous Arab raids that didn't have a lasting impact during the Byzantine era. For instance, sometime around 640 the Arab governor of Syria (and future Caliph of the Umayyad Caliphate) Mu'awiya I, may have had a year-long military excursion through Anatolia, during which he might have conquered the city. I'm putting "may" in there because I can't find multiple sources that agree with each other on the date of this raid.1
1 - Ostrogorsky says 641, but multiple other sources say he was busy conquering Palestine that year. If I had to take a guess, it would be that Ostrogorsky got his "Caeserea"s mixed up. However, Kegi agrees with Ostrogorsky that there may have been a raid around in 640 or 641 that started on the Mediterranean coast and wintered on the Black Sea.
Upvote:2
It seems possible that the location of the Arab/Byzantine battle you are thinking of wasn't Kayseri in Anatolia, but Caesarea Maritima in the Levant region. The confusion on the name is noted in the wiki article:
The Latin name Caesarea referred to a number of cities in the region, notably Caesarea near Mount Hermon and Caesarea the capital of Cappadocia. Whilst the name Caesarea was frequently used alone for the subject of this article, various markers were used to differentiate the location from these other locations; these include "Palestina" ("of Palestine"), "Maritima" ("by the sea"; Greek: Παράλιος Parálios), "Sebaste" and "Stratonis". "Palestina" is the most common term used in ancient sources, but since the creation of Israel in 1948 historians have tended to use the term less frequently.
We can see from the wikipedia article that Caesarea Maritima was indeed an active site during the byzantine and arab conquest
Caesarea remained the provincial capital throughout the 5th and 6th centuries. It fell to Sassanid Persia in the Byzantine–Sasanian War of 602–628, in 614, and was re-conquered by Byzantium in 625...Caesarea was lost for good by the Byzantines to the Muslim conquest in 640.
We can also note that Caesarea is mentioned during the Battle of the Yarmuk in 636 between the Byzantines and the Arab armies (emphasis mine)
Reinforcements were sent to Caesarea under Heraclius' son Constantine III, probably to tie down Yazid's forces, which were besieging the town.[26] The Byzantine imperial army moved out from Antioch and Northern Syria in the middle of June 636.
You can see we even have a Yazid involved here, though I don't think this is the one the OP indicated...
So I believe it is likely that a reference to a city Kayseri being involved in a battle between Byzantines and Arabs, might be referencing the Levantine city and not the Anatolian one.