  In this work we study the production of $K^*(4307)$ in $B$ decays by
determining the $J/\psi\pi^{+(0)}K^{0}$ and $J/\psi \pi^- K^+$ invariant mass
distributions of the processes $B^+\to J/\psi \pi^+\pi^0 K^0$ and $B^+\to
J/\psi \pi^+\pi^- K^+$, respectively. Such $K^*(4307)$ has been recently
predicted as a three-body state originated from the dynamics involved in the $K
D\bar D^*$ system, with the $KD$ subsystem forming the $D^{*}_{s0}(2317)$ in
isospin 0, and the $D\bar D^*$ subsystem generating the $X(3872)$ in isospin 0
and the $Z_c(3900)$ in isospin 1. The hidden charm content of $K^*(4307)$
favors its decay to a state like $J/\psi\pi K$ and the study of $B$-decays with
these particles in their final states can constitute a way of finding
experimental evidences for such an exotic vector meson, whose width, in spite
of its large mass, is still quite narrow (around 18 MeV).
