In this article, a general and effective method for designing compact bandpass filters (BPFs) with extensible orders and channels on a modified patch resonator is presented, for the first time. A comprehensive demonstration and validation of the proposed method are conducted, employing a circular patch resonator. First, the electric-field distributions under different mode resonances of a circular patch resonator are investigated. The TM $_{00}$ modes can be efficiently excited by loading a metal via at the center of the circular patch resonator. Interestingly, when dividing the modified circular patch resonator by magnetic walls along the radii, the resonant frequencies of the TM $_{00}$ mode in the resulting subresonators, are almost identical. These subresonators effectively suppress the excitation of higher order modes. Building upon this principle, second-, third-, and fourth-order BPFs with compact size and good stopband rejection are presented. Furthermore, by introducing multiple perturbed metal vias, BPFs with extensible channel numbers are developed. Dual-, tri-, and quad-channel BPFs with constant and compact size, wideband, and wide frequency range isolation are designed for verification. All measured results are in good agreements with the simulated ones, providing compelling evidence for the feasibility of the proposed design method.