During which geologic epoch did the homo mauritanicus species exist?

The correct answer is - Pleistocene.

The Homo mauritanicus is a hominid, a subspecies of the Homo erectus. The only specimen (or rather, part of it, as only a lower jaw is found) found from this subspecies of Homo erectus was found in North Africa, more specifically, in Morocco. The lower jaw found from this subspecies has been dated to 700,000 years of age.

The age of the Homo mauritanicus, by the only fossil found so far, suggests that this species lived in the Pleistocene epoch, which is the predecessor of the present day Holocene epoch. The stage age in which this fossil belongs is the 'Ionian'.