This is the area where some birth records will say child's name surname = mother's maiden name r father's surname. Did your grandfather have siblings? If so check their birth records. Otherwise the only solution is DNA testing. In this case Y testing from FTDNA may (or may not be) helpful. Also are there any family stories? This is really not that different from situations in the US where the father is unknown for whatever reason.
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Sarah L Meyer
Georgetown TX
ANK(I)ER, BIGOS, KARMELEK, PERLSTADT, STOKFISZ, SZPIL(T)BAUM, Poland
BIRGARDOVSKY, EDELBERG, HITE (CHAIT), PERCHIK Russia (southern Ukraine) and some Latvia or Lithuania
https://www.sarahsgenies.com