Baishin (indirect vassal) (陪臣)
Baishin refers to a name indicating a vassal of vassal in the samurai's relationship between lord and vassal. It was also called 'Matamono' or 'Matakerai' (indirect retainer).
Summary
Taking a present-day modern bureaucratic organization or corporate organization for instance, since some staff member is a 'subordinate to a section chief' and also a 'subordinate to a department director using such section chief as subordinate,' it is not very rare that the department director requests such staff member to perform duties not through the section chief, or that such staff member gives a report to the department director directly.
However, bushidan (samurai group), and a bureaucratic organization based on it in the bakufu (Japanese feudal government headed by a shogun) or each domain in the Edo period was only formed by a network of mutual relationship between lord and vassal in an individual clan. Therefore, for example, the Oishi family which was famous for Chushingura (The Treasury of Loyal Retainers) was a vassal of the Asano family of Ako Domain, but vassals of the Oishi family did not have a direct master-servant relationship with the Asano family. In this case, vassals of the Oishi family were baishin (indirect vassal) of the Asano family, and the Asano family did not have the right to directly give orders to vassals of the Oishi family.
In the office organization of the Edo bakufu, direct vassals of the Tokugawa Shogun family were called jikisan (immediate retainer), while the Shogun family called vassals of daimyo (Japanese feudal lord) and hatamoto (direct retainers of the Edo bakufu) 'baishin.'
This is why the aforementioned Oishi family was a vassal of the Asano family, but was baishin for the Tokugawa Shogun family. They were jikisan (immediate retainer) for daimyo and hatamoto, and were baishin for the Tokugawa Shogun family. And, their vassals were baishin for daimyo and hatamoto.
In the Edo period when the superior-inferior relationships were established, jikisan was permitted to have an audience with the shogun, but baishin was not permitted to have an audience with the shogun even if such baishin was Karo (chief retainer) whose clan had a daimyo-level yield of not less than 10,000 koku. They did not have a master-servant relationship with a shogun, and were not entitled to have an audience with the shogun.
Baishin could not directly meet with lords of other clans, either. When a lord was absent or could not come to the Edo-jo Castle by reasons of sickness or others, baishin sometimes came to castle and transmitted a message to the cabinet officials of the Shogunate such as roju (senior councilor of the Tokugawa shogunate) and wakadoshiyori (a managerial position in the Edo bakufu). At this time, the message was transmitted through 'goyotoritsugi' (an attendant to Shogun to announce a visitor and convey the message) because the cabinet officials of the Shogunate were also lords of other clans.
Great three baishin in the country
"Meisho Genkoroku" (the collections of anecdotes of great commanders in Japanese history) named great three baishin.
In spite of being baishin, Naoe Yamashiro (referring to Kanetsugu NAOE), Kobayakawa Saemon (referring to Takakage KOBAYAKAWA) and Hori Kenmotsuhai (referring to Naomasa HORI) were people were shikanemajiki although they maintained good order of the country.'
Kanetsugu NAOE, Takakage KOBAYAKAWA and Naomasa HORI were respectively a vassal of Kagekatsu UESUGI, Terumoto MORI and Hidemasa HORI whose lord was Hideyoshi TOYOTOMI and who were his direct retainers, which means that such three vassals were respectively equivalent to baishin of Hideyoshi TOYOTOMI, and therefore, the above evaluation was given to indicate that they could play a role even in maintaining good order of the country although they were baishin.