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[en] In this work, we use the QCD sum rule method to study the radiative decays of the vector and axial-vector mesons to each of the three charmed strange mesons, , and , through their dominant weak annihilation channels. We calculate all relevant transition form factors, which are used to estimate the branching fractions at different channels. The order of branching ratios are obtained to be in the order of - , which may be checked via different experiments.