  Motivated by the observed $P_{\psi s}^{\Lambda}(4459)/P_{\psi
s}^{\Lambda}(4338)$ and $T_{cc}(3875)^+$ states as the $\Xi_c \bar D^{*}/\Xi_c
\bar D$ and $DD^{*}$ molecular candidates, respectively, in this work we
investigate the $\Xi_c^{(\prime,*)} D^{(*)}$ molecular systems. We obtain the
mass spectra and the corresponding spatial wave functions of the
$\Xi_c^{(\prime,*)} D^{(*)}$-type double-charm molecular pentaquark candidates
with single strangeness, where we utilise the one-boson-exchange model and take
into account both the $S$-$D$ wave mixing effect and the coupled channel
effect. Our results show that the most promising candidates of the double-charm
molecular pentaquarks with single strangeness include the $\Xi_c D$ state with
$I(J^P)=0(1/2^-)$, the $\Xi_c^{\prime} D$ state with $I(J^P)=0(1/2^-)$, the
$\Xi_c D^{*}$ states with $I(J^P)=0(1/2^-,3/2^-)$, the $\Xi_c^{*} D$ state with
$I(J^P)=0(3/2^-)$, the $\Xi_c^{\prime} D^{*}$ states with
$I(J^P)=0(1/2^-,3/2^-)$, and the $\Xi_c^{*} D^{*}$ states with
$I(J^P)=0(1/2^-,3/2^-,5/2^-)$. To gain further insight into the inner
structures and the properties of the isoscalar $\Xi_c^{(\prime,*)} D^{(*)}$
molecular candidates, we utilize the constituent quark model to analyze their
M1 radiative decay behaviors and magnetic moments based on the obtained mass
spectra and spatial wave functions, which can offer the significant information
to determine their spin-parity quantum numbers and configurations in the
forthcoming experiments. We suggest that our experimental colleagues search for
the predicted $\Xi_c^{(\prime,*)} D^{(*)}$ molecular states.
