  Ultraperipheral collisions (UPCs) of protons and nuclei are important for the
study of the photoproduction of vector mesons and exotic states. The
photoproduction of vector mesons in the pentaquark resonance channel in
$p\mbox{-}Au$ UPCs at the Relative Heavy Ion Collider (RHIC) and $p$-$Pb$ UPCs
at the Large Hadron Collider (LHC) is investigated by employing STARlight
package. The cross sections of vector mesons via pentaquark state resonances
channel are obtained using effective Lagrangian method. The pseudo-rapidity and
rapidity distributions of $J/\psi $ and $\Upsilon(1S) $ are given for
$p\mbox{-}Au$ UPCs at the RHIC and $p$-$Pb$ at the LHC. It is found that the
RHIC is a better platform for discovering the pentaquark states than the LHC.
Moreover, $P_{b}(11080)$ is easier to identify than $P_c(4312)$ because the
background of $\Upsilon (1S)$ is weaker than $J/\psi$ in the $t$-channel at the
RHIC.
