Context: Methanol is thought to be mainly formed during the prestellar phase and its deuterated form keeps memory of the conditions at that epoch. Thanks to the unique combination of high angular resolution and sensitivity provided by ALMA, we wish to measure methanol deuteration in the planet formation region around a Class 0 protostar and to understand its origin. Aims: We mapped both the $^{13}$CH$_3$OH and CH$_2$DOH distribution in the inner regions ($\sim$100 au) of the HH212 system in Orion B. To this end, we used ALMA Cycle 1 and Cycle 4 observations in Band 7 with angular resolution down to $\sim$0.15$"$. Results: We detected 6 lines of $^{13}$CH$_3$OH and 13 lines of CH$_2$DOH with upper level energies up to 438 K in temperature units. We derived a rotational temperature of (171 $\pm$ 52) K and column densities of 7$\times$10$^{16}$ cm$^{-2}$ ($^{13}$CH$_3$OH) and 1$\times$10$^{17}$ cm$^{-2}$ (CH$_2$DOH), respectively. Consequently, the D/H ratio is (2.4 $\pm$ 0.4)$\times$10$^{-2}$, a value lower by an order of magnitude with respect to what was previously measured using single dish telescopes toward protostars located in Perseus. Our findings are consistent with the higher dust temperatures in Orion B with respect to that derived for the Perseus cloud. The emission is tracing a rotating structure extending up to 45 au from the jet axis and elongated by 90 au along the jet axis. So far, the origin of the observed emission appears to be related with the accretion disk. Only higher spatial resolution measurements however, will be able to disentangle between different possible scenarios: disk wind, disk atmosphere, or accretion shocks.< Réduire