In this paper, a novel and planar topology, which can be used to design notched-/dual-wideband bandpass filters (NWB/DWB BPFs) with controllable isolation bandwidth, is presented for interference rejection. Here, the isolation band is referred to notch band for NWB BPFs, while stopband between two passbands for DWB BPFs. The proposed topology is started from a novel T-shaped resonator with two poles and three zeros. Then, a pair of parallel-coupled lines and two open-ended stubs is added. With the help of the added parts, the extra four poles are introduced, and another two zeros are suppressed or excited according to whether it is required to realize a notched- or dual-band response. Due to the existence of multiple transmission poles and zeros, the excellent filtering responses, i.e., high isolation level, sharp selectivity, and good passband flatness, can be achieved. Besides, it is found that the isolation bandwidth of BPFs based on the proposed topology can be continuously varied from a narrow notch band to a wide stopband while the outer two passband edges are maintained unchanged by using suitable para-meters. To validate this, two prototypes are designed and measured, including a six-mode NWB BPF with 3-dB passband fractional bandwidth (FBW) of 94.1% and 20-dB notch FBW of 2.39%, and a three-mode DWB BPF with 3-dB passband FBWs of 36.2% and 22.6% and 20-dB stopband FBW of 14.5%.