It is unlikely that your story has anything to do with Kosice (Kassa, Kaschau). Rather I believe the lead is to the war of Hungarian independence of 1848. The leader of the Hungarian independence movement in this war (of 1848/49) was Lajos (Ludwig) von Kossuth (your Cashut!). The Austrians, weakened by their own uprising in Vienna of 1848, first contracted the Ban of Croatia, Joseph von Jellasich, to march on Budapest. After the Austrians recovered from their own revolution and enlisted the Tsar of Russia to squeeze the Hungarians from east and west, the Hungarian uprising of Kossuth was crushed and many of the Hungarian military leaders were executed. Kossuth and his closest aides and soldiers fled to Turkey (!!) where they lived for a while (from 1849). However, Kossuth later made triumphant visits to England and the United States (!) where he received ovations as a champion of liberty. Kossuth then lived in exile in England and Italy, and died in Turin.
Kossuth is one of the most popular figures of the Hungarian history. A lot has been published about him. He himself wrote the "Memoirs of my Exile." I wonder whether your ancestors might be mentioned there.
Try to post your query at the Hungarian board and ask for historians to help you further.