Liushanmen means 'Six Doors'. It is a popular name for government law-enforcement offices, used loosely in Chinese fiction and drama for the world of constables and magistrates as opposed to the jianghu. Its exact historical scope is debated, so it is best read as a storyteller's term. Under the Power uses it for the constable side of its cases.
Where it comes up

Silk & Schemes
Under the Power: A Ming-Dynasty Secret Police Officer, a Constable and 55 Episodes of Cases
A guide to the 2019 Ming-dynasty mystery romance Under the Power: Ren Jialun as a feared Embroidered Uniform Guard officer, Tan Songyun as the constable assigned to him, the real court history behind the cases, and how viewers split on a 55-episode run.