Developing small-scale continuum catheter robots with inherent soft bodies and high adaptability to different environments holds great promise for biomedical engineering applications. However, current reports indicate that these robots meet challenges when it comes to quick and flexible fabrication with simpler processing components. Herein, we report a millimeter-scale magnetic-polymer-based modular continuum catheter robot (MMCCR) that is capable of performing multifarious bending through a fast and general modular fabrication strategy. By preprogramming the magnetization directions of two types of simple magnetic units, the assembled MMCCR with three discrete magnetic sections could be transformed from a single curvature pose with a large tender angle to a multicurvature S shape in the applied magnetic field. Through static and dynamic deformation analyses for MMCCRs, high adaptability to varied confined spaces can be predicted. By employing a bronchial tree phantom, the proposed MMCCRs demonstrated their capability to adaptively access different channels, even those with challenging geometries that require large bending angles and unique S-shaped contours. The proposed MMCCRs and the fabrication strategy shine new light on the design and development of magnetic continuum robots with versatile deformation styles, which would further enrich broad potential applications in biomedical engineering.