The mass and meson-current coupling constant of the resonance $X(5568)$, as well as the width of the decay $X(5568)to B_s^{ast}pi$ are calculated by modeling the exotic $X(5568)$ resonance as a diquark-antidiquark state $% X_b=[su][bd]$ with quantum numbers $J^{P}=1^{+}$. The calculations are made employing QCD two-point sum rule method, where the quark, gluon and mixed vacuum condensates up to dimension eight are taken into account. The sum rule approach on the light-cone in its soft-meson approximation is used to explore the vertex $X_bB_{s}^{ast}pi$ and extract the strong coupling $% g_{X_bB_{s}^{ast}pi}$, which is a necessary ingredient to find the width of the $X_b to B_s^{ast}pi^{+}$ decay process. The obtained predictions are compared with the experimental data of the D0 Collaboration, and results of other theoretical works.
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