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Identifying the nature and origin of dark matter is one of the major challenges for modern astro and particle physics. Direct dark-matter searches aim at an observation of dark-matter particles interacting within detectors. The focus of several such searches is on interactions with nuclei as provided e.g. by weakly interacting massive particles. However, there is a variety of dark-matter candidates favoring interactions with electrons rather than with nuclei. One example are dark photons, i.e., long-lived vector particles with a kinetic mixing to standard-model photons. In this work we present constraints on this kinetic mixing based on data from CRESST-II Phase 2 corresponding to an exposure before cuts of 52 kg-days. These constraints improve the existing ones for dark-photon masses between 0.3 and 0.7 keV/c$^2$ .