Here, we present a detailed study on the magnetic, magneto-transport, and magneto-thermal properties of the equiatomic half-Heusler compounds with the general formula, RPdSi (R = Y and rare-earth, Gd-Er). These materials crystallize in two different superstructures of the TiNiSi-type orthorhombic unit cell with the space groups Pnma and Pmmn. Our magnetic and heat capacity measurements reveal the onset of an antiferromagnetic (AFM) ordering in the temperature range 3-16 K for all the local moments bearing RPdSi compounds, while the non-magnetic analog, YPdSi exhibits a Pauli-paramagnetic behaviour. The AFM state of these compounds can be tuned by magnetic field and temperature as demonstrated by the magnetic measurements below the Neel temperature (T N ). Most importantly, this tuning of the magnetic structure is well documented in the complex temperature and field dependence of magnetoresistance (MR) and magnetocaloric effect (MCE). Our study establishes a striking correlation of the commensurate/incommensurate AFM structure with that of positive/negative MR and MCE in this series of compounds. We emphasize that such a framework applies to a large number of AFM intermetallic systems.