This "A Certain Killer" is a transposition, for the time, of the myth of the murderous and solitary samurai, also very popular in French cinema of the sixties, as in Jean-Pierre Melville's detective stories, "Le Samourai", from the same year (the title clearly reveals the source of inspiration) is a good example.
Basically, the mythology is ancient and comes from the old ronin of feudal Japan, lost samurai, without a master, the Daimyo, and therefore prevented from living an honorable life according to the Bushido, the samurai code of honor. Nor could they even take their own lives through seppuku (honor-restoring action), being condemned to a dishonorable life.
This myth inspired Kurosawa, it inspired Leone and many westerns, it inspired Melville, it inspired Tarantino, it even inspired Jarmusch, and it also inspired some new wave Japanese cinema, which transposed the myth to contemporary times.
These killers are modern samurai, subject to their own code of honor, but without prejudice in placing themselves at the service of any mafia boss, to commit criminal acts from which, invariably, only they or their friends benefit. They only punish those who deserve it, but generally include in the punishment those who use them, even paying generously, for dishonorable acts.
If the myth is old and has already given rise to many memorable works, and not just in cinema, this film is certainly not one of the best examples. It's not that it's bad, but it's banal, with nothing to distinguish it.
This samurai did not make a school or leave any disciples. It's pure entertainment, in the style of the period.