Is this already an Americanized version of your ancestor's surname? In this form sure does not seem Slavic - Ruthenian.
map of Austria-Hungary empirehttp://users.erols.com/mwhite28/austhung.htmhttp://lazarus.elte.hu/hun/maps/1910/vmlista.htmhttp://brainworker.ch/Oesterreich/Austria-hungary.png
do tell us if a region like Galicia was ever mentioned.
Was your ancestor naturalized citizen? Did he have social security numbers?
Beretski could be a location Bereska, Galicia
or a name of county Bereg in old Hungary.