The strong coupling constants, g_D_sDK_0^*, g_B_sBK_0^*, g_D^∗_sD K, g_B^∗_sBK, g_D^∗_sD K_1 and g_B^∗_sBK_1, where K_0^*, K and K_1 are scalar, pseudoscalar and axial vector kaon mesons, respectively are calculated in the framework of three-point QCD sum rules. In particular, the correlation functions of the considered vertices when both B(D) and K_0^*(K)(K_1) mesons are off-shell are evaluated. In the case of K_1, which is either K_1(1270) or K_1(1400), the mixing between these two states are

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... also taken into account. A comparison of the obtained result with the existing prediction on g_D^∗_sD K as the only coupling constant among the considered vertices, previously calculated in the literature, is also made.