  We have investigated the process $J/\psi \to {\bar{K}}^0K^+\rho^-$ by taking
into account the $S$-wave ${K^*\bar{K}^*}$, $\rho \omega$, and $\rho \phi$
final-state interactions, where the scalar meson $a_0(1710)$ is generated. In
addition, we also take into account the contributions from the scalar
$a_0(980)(\to \bar{K}^0K^+)$ and the intermediate resonances $K_1(1270)^{-}(\to
{\bar{K}}^0\rho^-) $ and $K_1(1270)^{0}(\to K^+\rho^-)$. Our results show that,
in the ${{\bar{K}}^0K^+}$ invariant mass distribution, a clear peak structure
around 1.8~GeV appears, which could be associated with the scalar $a_0(1710)$,
however, no significant structure of the $a_0(980)$ is observed. On the other
hand, one can find clear peaks of the $K_1(1270)$ in the ${\bar{K}}^0\rho^-$
and $K^+\rho^-$ invariant mass distributions. The future precise measurement of
this process by the BESIII and Belle II Collaborations and the planned Super
Tau-Charm Facility (STCF) in the future could shed light on the nature of
$a_0(1710)$.
