We have arriving thru NY Ellis Island from location Gyorkony:
Steiner, Andreas Gyorkony, Hungaryy 33 1881 1914
Stiener, Andras Gyorkony 26 1875 1901
Stinner, Eva Gyorkony 22 1879 1901
Stiener, Paul Gyorkony, Hungary 0 1909 1909 [infant] Is this your ancestor? He, mother and a brother listed as Hungarian. I would think if they were Hebrew that would on the arrival manifest.
http://www.gyorkony.hu/NEW/http://www.maplandia.com/hungary/tolna/gyorkony/