This work is a continuation of Paper I [Sharykin et al., 2018] devoted to analysis of nonthermal electron dynamics and plasma heating in the confined M1.2 class solar flare SOL2015-03-15T22:43 revealing energy release in the highly sheared interacting magnetic loops in the low corona, above the polarity inversion line (PIL). The scope of the present work is to make the first extensive quantitative analysis of the photospheric magnetic field and photospheric vertical electric current (PVEC) dynamics in the confined flare region near the PIL using new vector magnetograms obtained with the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) with high temporal resolution of 135 s. Data analysis revealed sharp changes of the magnetic structure and PVEC associated with the flare onset near the PIL. It was found that the strongest plasma heating and electron acceleration were associated with the largest increase of the magnetic reconnection rate, total PVEC and effective PVEC density in the flare ribbons. Observations and non-linear force-free field (NLFFF) extrapolations showed that the magnetic field structure around the PIL is consistent with the tether-cutting magnetic reconnection (TCMR) geometry. We gave qualitative interpretation of the observed dynamics of the flare ribbons, magnetic field and PVEC, and electron acceleration, within the TCMR scenario.