GaToroid, a novel configuration for hadron therapy gantry, is based on superconducting coils that gen- erate a toroidal magnetic field to deliver the beam onto the patient. Designing the complex GaToroid coils requires careful consideration of the local beam optical effects. We present a Python-based tool for charged particle transport in complex electromagnetic fields. The code implements fast tracking in arbitrary three-dimensional field maps, and it is not limited to specific or regular reference trajectories, as is generally the case in accelerator physics. The tool was used to characterise the beam behaviour inside the GaToroid system. It automatically determines the reference trajectories in the symmetry plane and analyses three-dimensional beam dynamics around these trajectories. Beam optical parameters in the field region were compared for various magnetic configurations of GaToroid. This paper introduces the new tracker and shows the benchmarking results. Furthermore, first- order beam optics studies for different arrangements demonstrate the main code features and serve for the design optimisation