We report on the observation and comprehensive study of the terahertz radiation induced magneto-photogalvanic effect (MPGE) in bulk CdHgTe crystals hosting Kane fermions. The MPGE has been detected in CdxHg1-xTe films with Cd contents x = 0.15 and 0.22 subjected to an in-plane magnetic field. At liquid helium temperature we observed multiple resonances in MPGE current upon variation of magnetic field. In the x = 0.22 with noninverted band structure, the resonances are caused by cyclotron resonance (CR) and photoionization of an impurity level. In the x = 0.15 films with an inverted band structure, they originate from the CR and interband optical transitions. Band structure calculated by the Kane model perfectly describes positions of all resonances. In particularly, the resonant MPGE caused by interband transitions excited by THz radiation is caused by the gapless energy spectrum of Kane fermions realized in materials with certain Cd contents and temperature range. In addition to the resonant MPGE current we detected a nonresonant one due to indirect optical transitions (Drude-like). This contribution has a nonmonotonic magnetic field dependence increasing linearly at low magnetic field B, approaching a maximum at moderate field and decreasing at high B. While the nonresonant MPGE decreases drastically with increasing temperature, it is well measurable up to room temperature. The developed theory demonstrates that the MPGE current arises due to cubic in momentum spin-dependent terms in the scattering probability. The asymmetry caused by these effects results in a pure spin current which is converted into an electric current due to the Zeeman effect