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For a normalized root system $R$ in $\mathbb R^N$ and a multiplicity function$k\geq 0$ let $\mathbf N=N+\sum_{\alpha \in R} k(\alpha)$. Let $L=-\Delta +V$,$V\geq 0$, be the Dunkl--Schr\"odinger operator on $\mathbb R^N$. Assume thatthere exists $q >\max(1,\frac{\mathbf{N}}{2})$ such that $V$ belongs to thereverse H\"older class $\text{RH}^q(dw)$. We prove the Fefferman--Phonginequality for $L$. As an application, we conclude that the Hardy space$H^1_{L}$, which is originally defined by means of the maximal functionassociated with the semigroup $e^{tL}$, admits an atomic decomposition withlocal atoms in the sense of Goldberg, where their localization are adapted to$V$.

Schr\"odinger operators with reverse H\"older class potentials in the Dunkl setting and their Hardy spaces