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I don't know if this will be of any help to you but the Polish name Czerniak comes from the root czarn which means black or dark. Perhaps they are related. Sternick may be an anglicized or americanized spelling (many Polish immigrants had their surnames respelled to fit better with English pronounciations).

Your surname could be a variant of Pain or Paine that comes from the latin "pagan". the meaning is "not christian"

See Dictionary of surnames - Basil Cottle