In this work, we study deuterium fractionation in four starless cores in the low-mass star-forming region L1688 in the Ophiuchus molecular cloud. We study how the deuterium fraction (RD) changes with environment, compare deuteration of ions and neutrals, core centre and its envelope, and attempt to reproduce the observed results with a gas-grain chemical model. We chose high and low gas density tracers to study both core centre and the envelope. With the IRAM 30 m antenna, we mapped N_2_H+(1-0), N_2_D+(1-0), H^13^CO+ (1-0) and (2-1), DCO+(2-1), and p-NH_2_D(111-101) towards the chosen cores. The missing p-NH3 and N_2_H+(1-0) data were taken from the literature. To measure the molecular hydrogen column density, dust and gas temperature within the cores, we used the Herschel/SPIRE dust continuum emission data, the Green Bank Ammonia Survey data (NH3), and the COMPLETE survey data to estimate the upper limit on CO depletion. We present the deuterium fraction maps for three species towards four starless cores. Deuterium fraction of the core envelopes traced by DCO+/H^13^CO+ is one order of magnitude lower (~0.08) than that of the core central parts traced by the nitrogen-bearing species (~0.5). Deuterium fraction increases with the gas density as indicated by high deuterium fraction of high gas density tracers and low deuterium fraction of lower gas density tracers and by the decrease of RD with core radii, consistent with the predictions of the chemical model. Our model results show a good agreement with observations for RD(N_2_D+/N_2_H+) and RD(DCO+/HCO+) and underestimate the RD(NH_2_D/NH_3_).