Summary: We consider a smoothly bounded \(q\)-pseudoconvex domain \(\Omega\) in an \(n\)-dimensional Stein manifold \(X\) and suppose that the boundary \(b\Omega\) of \(\Omega\) satisfies \((q-P)\) property, which is the natural variant of the classical \(P\) property. Then, one prove the compactness estimate for the \(\bar\partial\)-Neumann operator \(N_{r,s}\) in the Sobolev \(k\)-space. Applications to the boundary global regularity for the \(\bar\partial\)-Neumann operator \(N_{r,s}\) in the Sobolev \(k\)-space are given. Moreover, we prove the boundary global regularity of the \(\overline{\partial}\)-operator on \(\Omega\).