In Suhl at this time were several small firms specialized in mounting and also specialized in mounting parts. So this can be the mark of an gunsmith or an specialized provider, its not that rare to find this kind of markings on mountings.
The first thought by me for "O.Sch." was Otto Scherell, well known gunsmith in Berlin and Delitsch/Saxonia, but this makes not big sense with Kerner as signed retailer. However, it is possible that Scherell did the mounting later if the rifle was not sold with mounts.Its just one of the many possible options..............
A lot is conceivable, and a lot is immersed in history.