We explore a new approach to search for a low-mass $Z^{\prime}$ particle through $J/\psi$ decays by identifying its existence through parity-violating phenomena in the isospin-violating final states of $\Lambda\overline{\Sigma}^{0}$ and the corresponding charge conjugated states of $\overline{\Lambda}\Sigma^{0}$. 
Our investigation centers on a generation-independent and leptophobic $Z^{\prime}$ with its mass below 10 GeV.
Given the present experimental conditions at the Beijing Spectrometer III~(BESIII) and the anticipated opportunities at the Super Tau Charm Factory~(STCF), we conduct Monte-Carlo simulations to predict possible events at both facilities.
Notably, we foresee a substantial enhancement in the precision of the lower limit estimation of $\alpha_{\text{NP}}$ as well as a reduction in statistical uncertainty with upcoming STCF experiments.
Furthermore, it is essential to highlight that a null result in the measurement of $\alpha_{\text{NP}}$ would impose stringent constraints, requiring the $Z^{\prime}-q-q$ couplings to be on the order of $10^{-2}$. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.