We present a type of few-period helically twisted all-solid photonic bandgap fiber (AS-PBGFs). The helical structure leads to orbital resonance of a cladding rod light, which couples with the core mode. A two-period twist structure exhibits an extremely strong resonant dip of up to 30 dB. A series of samples with twist periods of 3.31-7.92 mm (yielding twist rates of 1.90-0.79 rad⋅mm-1) in association with different resonance orders are fabricated and demonstrated. The inherent physical mechanism underlying the resonance is analyzed. Moreover, the responses of the resonance to mechanical torsion, strain, and temperature are investigated. The twisted AS-PBGFs feature high reproducibility, stability, and robustness, and have great potential in tunable in-fiber filters and sensors.