  Recently BESIII collaboration discovered a charged strange hidden-charm state
$Z_{cs}$(3985) in the $D_s^-D^{*0} + D_s^{*-}D^{0}$ spectrum. A higher
$Z'_{cs}$ state coupling to $\bar{D}_s^{*-}D^{*0}$ is expected by SU(3)-flavor
symmetry, and their bottom partners are anticipated by heavy quark flavor
symmetry. Here we study the photoproduction of these exotic states and
investigate carefully the background from Pomeron exchange. Our results
indicate that the maximal photoproduction cross section of strange partner is
around 1 $\sim$ 2 orders of magnitude smaller than that of the corresponding
non-strange states. The possibility of searching for them in future
electron-ion colliders (EIC) is briefly discussed.
