I have a question. I am still doing research, but I know I could get the answer faster here. The Turks who overran Hungary during the Tartar invasions of the 1400s. Were they Muslim? If so, did Hungary have Middle Eastern influence at that time?
In 1451 the Ottoman Empire of the Turks stretched as far west as to have obsorbed most of Greece, north to the Danube in Bulgaria, up the Danube to Odessa on the Black Sea, down to Constantinople and across most of Anatolia (Asia Minor/Turkey).
There must certainly have been raids by Turks and Tartars (allies) in the later 1400s, because:
By 1503 the Ottoman Empire north of Greece has been extended north-northeast through all of Bosnia and west from there to Belgrade, forming a frontier with Hungary. The Turks breach that frontier from time to time between and by 1566 they absorb most of Hungary.
By 1566 the states and principalities on the empire's northwestern and northernmost borders pay tribute to the Sultan (from Croatia up into Poland just south of Cracow and east across the Caucasus north of the Black Sea.
I hope this helps.
"If so, did Hungary have Middle Eastern influence at that time?"
Sorry, in addition to the "conquest" info, the answer to your question is "yes".