Your information points to the town of Schandorf in Burgenland/Austria. A previous other German name for the town was Schöndorf.
When Burgenland was still part of Hungary (till the end of 1921), the official Hungarian name of the town was Csém. The inhabitants were mostly ethnic Croats.
The last name Schomogyi is Hungarian where it was spelled Somogyi.
I guess that the town of Schandorf has a web site where you could try to make contact and hopefully find living relatives. You should also visit the web site of the Burgenland Bunch.