  We perform a theoretical study of the $J/\psi \to \omega (\phi) K^* \bar{K} +
c.c. \to \omega (\phi) K^0 \pi^+ K^-$ reactions with the assumption that the
$f_1(1285)$ is dynamically generated from a single channel $K^* \bar{K} + c.c$
interaction in the chiral unitary approach. Two peaks in the $K^0 \pi^+ K^-$
invariant mass distribution are observed, one clear peak locates at the
$f_1(1285)$ nominal mass, the other peak locates at around $1420\; \rm MeV$
with about $70 \;\rm MeV$ width. We conclude that the former peak is associated
with the $f_1(1285)$ and the latter peak is not a genuine resonance but a
manifestation of the kinematic effect in the higher energy region caused by the
$K^* \bar{K} + c.c.$ decay mode of the $f_1(1285)$.
