  We are systematically studying the electromagnetic characteristics of
multiquark systems to shed light on their internal structure, whose nature and
quantum numbers are controversial. In this study, we investigate the magnetic
dipole, electric quadrupole, and magnetic octupole moments of the $\Xi_c^*\bar
K$ state within the context of the QCD light-cone sum rule. During this
analysis, we posit that the $\Xi_c^*\bar K$ state assumes a molecular structure
with quantum numbers $J^P = \frac{3}{2}^-$. The extracted outcomes are given as
$\mu_{\Xi_c^*\bar K} = 0.15^{+0.04}_{-0.03}\,\mu_N$, $\mathcal{Q}_{\Xi_c^*\bar
K} = (-0.93^{+0.22}_{-0.17})\times 10^{-3}\,\rm{fm^2}$, and
$\mathcal{O}_{\Xi_c^*\bar K} = (-0.45^{+0.10}_{-0.09})\times
10^{-4}\,\rm{fm^3}$. The findings of this study, when considered alongside
other pertinent characteristics, may assist in elucidating the nature of this
controversial phenomenon.
