We analyze the modifications that a dense nuclear medium induces in the Ds0⁎(2317)± and Ds1(2460)±. In the vacuum, we consider them as isoscalar D(⁎)K and ▪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(⁎), ▪, K, and ▪ develop when embedded in a nuclear medium. Although particle-antiparticle Ds0,s1(⁎)(2317,2460)+versusDs0,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/▪ molecular content, and discuss how this novel feature can be used to better determine/constrain the inner structure of these exotic states.