The щ letter is common to three Slavic languages (Russian, Ukrainian and Bulgarian), and has different pronunciations in each: the accepted Russian pronunciation is a soft "sh" sound (anything else is considered a regional variation or non-standard); Ukrainian pronunciation is closer to a "sh-ch" combination, sounding very much like Polish SZCZ; Bulgarian speakers pronounce this letter "sht". In all cases, this is a single phoneme, especially in situations where (as in Russian) щ appears as the result of a consonant mutation (for example, the present tense first person singular for the verb "to search", where ск [sk] becomes щ [shch] (искать --> ищу).
The spelling of Jewish surnames, as we've all no doubt seen before, could be widely variable, depending on the native language of the person keeping the record. The surname of my maternal grandmother was spelled Olsztajn, Olsztejn, Olstein in Polish and Ольштейнъ, Ольштайнъ in Russian (after April, 1876) in metrical documents, occasionally with variant spellings in the same record. And that was in Poland -- when different family members emigrated to North America, there were half-a-dozen different ways the surname was Anglicized. My point is that it's important to be a bit flexible when considering how an ancestor's name was spelled or pronounced.
Researching: NOVITSKIY (Kyiv, Vasil'kiv/Ukraine), OHLSTEIN/OLSZTEJN (Łowicz, Łódź/Poland), GEJMAN/HYMAN (Ashmyany/Belarus), POTASNIK/LEVY (Who knows?)