What you know KOSTKA in Matiasovce's phone book.

http://telefonny.zoznam.sk/kostka/slovensko/predvolba=052/

Is the "adopted" a family story? If yes, those family stories can take a life of their own. Not saying that what you were told about "adopted" is not true. Adopted - when?
Trust but verify.

Kosztka, Bela Matyasfalu 17 1886 1903
Kosztka, Jozsef Matyassoz 30 1872 1902
Kosztka, Katalin Matyasfalu 15 1887 1902
source: www.ellisislandrecords.org