Scherek and variants are well represented in the large town of Posen in the 1800's. They appear in early records of Naturalized Jewish Citizens as documented in Eduard Flottwell's lists which are also translated into English by Edward David Luft in The Naturalized Jews of the Grand Duchy of Posen in 1834 and 1835, Second Edition, Avotaynu 2004, about $50 USD paperback book.
See:Heinrich EDUARD von Flottwell
See: Geni Jewish Town Project for Posen.