It s no secret that for the biggest part of their modern history the entirety of what is today known as Greece, Romania, Bulgaria, Hungary, all the formerly Yugoslavian nation fragments, sizable parts of Poland, Austria, Czechia and Slovakia, in summary the whole of Balkans and considerable parts of Eastern Europe were under Turkish rule.
Just to put that right briefly ...
I can be wrong but as far as I know there have never been (important) parts of Austria under Turkish rule. The Ottoman Empire tried twice to besiege the city of Vienna, but failed each time devastatingly. The first siege took place in
1529, the second in
1683, both times the Ottoman Empire failed to gain a foothold in Austria.
But it is actually true that Turkish civilization had an impact in Austria. For example, the Austrians got to know coffee through the sieges (and love it, Austria is well known for its coffee house culture), the so-called "Butterkipferl" also dates from this time and is a pastry that ridicules the Turkish crescent.