Under the Han dynasty, an official of the rank of two thousand dan who had served for three years could recommend one son or younger brother for appointment as a court gentleman. The practice was called renzi (任子), “appointing a son.” It is also known as menyin (门荫), “the shade of the gate.”
Chinese Wikipedia describes it as “a privilege system” that gave rank to the sons, grandsons, younger brothers or nephews of high officials, according to the official’s own rank. The rank was lower than the father’s. Sometimes it was only a title, or simply the right to enter service.