Based on D. Catlin's work, Property $(P_q)$ of the boundary implies the compactness of the $\bar{\partial}$-Neumann operator $N_q$ on smooth pseudoconvex domains. We discuss a variant of Property $(P_q)$ of the boundary of a smooth pseudoconvex domain for certain levels of $L^2$-integrable forms. This variant of Property $(P_q)$ on the one side, implies the compactness of $N_q$ on the associated domain, on the other side, is different from the classical Property $(P_q)$ of D. Catlin and Property $(\widetilde{P_q})$ of J. McNeal.