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Abstract In this paper we study the impact of a scalar exchange on the dark matter relic abundance by solving a plasma-modified Schrödinger equation. A simplified model is considered where a Majorana dark matter fermion is embedded in a U(1)′ extension of the Standard Model and couples with a dark Higgs via a Yukawa interaction. We find that the dark-Higgs exchange can increase the overclosure bounds significantly. For the largest (smallest) value of the Yukawa coupling examined in this work, the dark matter mass is lifted from 5 TeV (0.55 TeV) to 27 TeV (0.70 TeV).