  Using the one-boson-exchange model, we investigate the interactions between
the doubly charmed baryon $\Xi_{cc}(3621)$ and the $S-$wave (anti-)kaon
accounting for the $S-D$ wave mixing and coupled-channel effects. We find the
coupled $\Xi_{cc}K/\Xi_{cc}K^*$ state with $I(J^P)=0(1/2^-)$, the $\Xi_{cc}K^*$
state with $0(1/2^-)$, the $\Xi_{cc}\bar{K}$ state with $0(1/2^-)$, and the
$\Xi_{cc}\bar{K}^*$ states with $0(1/2^-,3/2^-)$ can be recommended as good
doubly charmed molecular candidates with strangeness $|S|=1$. We further
examine their M1 radiative decay behaviors and magnetic moments within the
constituent quark model framework. This information can enhance our
understanding of their inner structures, including the distribution of electric
charge and the orientation of the constituent quarks' spins.
