In the present work, samarium (Sm)-modified YCrO$_3$ nanoparticles have been investigated. The pristine and Sm-doped YCrO$_3$ nanoparticles were synthesized by the sol–gel method. The phase purity and microstructure of the nanoparticles were analysed by X-ray diffraction (XRD), transmission electron microscope (TEM) investigations. To understand the detailed charge transport mechanism, dc and ac electrical properties were measured. The dc electrical conductivity was found to arise due to an adiabatic small polaronic conduction mechanism. On the other hand, the correlated barrier hopping (CBH) conduction model is used to explain the ac conduction process as a function of frequency (20 Hz–1 MHz) and temperature (298–523 K). The dielectric behaviour of the nanoparticles is followed by the modified Cole–Cole model. With the increase in Sm doping, dielectric permittivity and both free charge and space charge conductivity values increase. The shifting of the peak with frequency in ${\varepsilon}'$ vs. temperature curve, confirmed the existence of a relaxor-like ferroelectric behaviour in the doped YCrO$_3$ nanoparticles. The clear hysteresis loop observed at 80 K delineates the ferromagnetic ordering in the chromate system. The magnetic study suggests that magnetization values increase due to Sm doping. The observation of magneto-dielectric constant in the investigated nanoparticles opens up its potentiality for future spintronics devices.