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Inspired by the observation of the doubly charmed tetraquark state $T_{cc}^+$at the LHCb Collaboration, we systematically study the $S$-wave interactionsbetween a pair of charmed mesons ($D_{1},\,D_{2}^{\ast}$) in the $T$-doublet,where we adopt the one-boson-exchange model and consider both the $S$-$D$ wavemixing and coupled channel effects. Our numerical results suggest that theprime doubly charmed molecular tetraquark candidates are the $S$-wave $D_1D_1$state with $I(J^P)=0(1^+)$, the $S$-wave $D_1{D}_2^{\ast}$ states with$I(J^P)=0(1^+,\,2^+,\,3^+)$, and the $S$-wave ${D}_2^{\ast}{D}_2^{\ast}$ stateswith $I(J^P)=0(1^+,\,3^+)$. The $S$-wave $D_1D_1$ state with $I(J^P)=1(2^+)$,the $S$-wave $D_1{D}_2^{\ast}$ state with $I(J^P)=1(3^+)$, and the $S$-wave${D}_2^{\ast}{D}_2^{\ast}$ state with $I(J^P)=1(4^+)$ may be the possibleisovector doubly charmed molecular tetraquark candidates. We expect theexperiments like the LHCb or Belle II collaborations to search for thesepredicted doubly charmed molecular tetraquarks near the $D_1D_1$, $D_1D_2^*$,and $D_2^*D_2^*$ thresholds in future.

A new group of doubly charmed molecule with $T$-doublet charmed meson pair