  We analyze the modifications that a dense nuclear medium induces in the
$D_{s0}^\ast(2317)^\pm$ and $D_{s1}(2460)^\pm$. In the vacuum, we consider them
as isoscalar $D^{(*)}K$ and $\overline{D}{}^{(*)}\overline{K}$ $S$-wave bound
states, which are dynamically generated from effective interactions that lead
to different Weinberg compositeness scenarios. Matter effects are incorporated
through the two-meson loop functions, taking into account the self energies
that the $D^{(*)}$, $\overline{D}{}^{(*)}$, $K$, and $\overline{K}$ develop
when embedded in a nuclear medium. Although particle-antiparticle
[$D^{(\ast)}_{s0,s1}(2317,2460)^+$ versus $D^{(\ast)}_{s0,s1}(2317,2460)^-$]
lineshapes are the same in vacuum, we find extremely different density patterns
in matter. This charge-conjugation asymmetry mainly stems from the very
different kaon and antikaon interaction with the nucleons of the dense medium.
We show that the in-medium lineshapes found for these resonances strongly
depend on their $D^{(*)}K$/$\overline{D}{}^{(*)}\overline{K}$ molecular
content, and discuss how this novel feature can be used to better
determine/constrain the inner structure of these exotic states.
