The ballistic filtering property of nanoscale crosses was used to investigate the effect of perpendicular magnetic fields on the ballistic transport of electrons on wide band-gap GaN heterostructures. The straight scattering-less trajectory of electrons was modified by a perpendicular magnetic field which produced a strong non-linear behavior in the measured output voltage of the ballistic filters and allowed the observation of semi-classical and quantum effects, such as quenching of the Hall resistance and manifestation of the last plateau, in excellent agreement with the theoretical predictions. A large measured phase coherence length of 190 nm allowed the observation of universal quantum fluctuations and weak localization of electrons due to quantum interference up to similar to 25 K. This work also reveals the prospect of wide band-gap GaN semiconductors as a platform for basic transport and quantum studies, whose properties allow the investigation of ballistic transport and quantum phenomena at much larger voltages and temperatures than in other semiconductors. Published by AIP Publishing.