  We investigate $DD^*$ and $D\bar{D}^*$ momentum correlations in high-energy
collisions to elucidate the nature of $T_{cc}$ and $X(3872)$ exotic hadrons.
Single range Gaussian potentials with the channel couplings to the isospin
partners are constructed based on the empirical data. The momentum correlation
functions of the $D^0D^{*+}$, $D^+D^{*0}$, $D^0\bar{D}^{*0}$, and $D^+D^{*-}$
pairs are computed with including the coupled-channel effects. We discuss how
the nature of the exotic states are reflected in the behaviors of the
correlation results.
