The essential normality of analytic Hilbert modules is a central problem in the geometric analysis of Hilbert modules. The essential normality of quasi-homogeneous quotient modules over the polydiscs has been characterized, which is deeply related to the distinguished varieties. We are concerned about the essential normality of inhomogeneous distinguished quotient Hardy modules over the polydiscs, and give a positive answer in the case that the associated ideal is radical and regular along the boundary of the associated variety.
