The present study focuses on the response of a near-wall turbulent flow subjected to a spatially localized body force. Characteristics of a turbulent channel flow under a Lorentz force distribution are analysed through Direct Numerical Simulation at a low turbulent Reynolds number (4200) and a low magnetic Reynolds number. It is found that streamwise or spanwise magnetic fields alter only slightly the wall layer when the magnetic fields are constrained within the buffer layer. Yet, the turbulent wall layer is greatly affected once the edge of the localized Lorentz force reaches the logarithmic layer. Furthermore, the spanwise magnetic field results in flow relaminarization at much lower magnetic severity parameters than the streamwise magnetic field. We further show that this is basically coming from the specific MHD terms appearing in the shear-stress transport equations. Tables 1, Figs 6, Refs 5.