  We present an improved calculation of the $HHV$ ($H=D_{(s)},\, B_{(s)}$, $V=
\rho$, $K^\ast$, $\omega$, and $\phi$) coupling constants $g_{HHV}$ beyond
leading order in $\alpha_s$ from QCD light-cone sum rules (LCSRs) by means of
the light-cone distribution amplitudes (LCDAs) of light vector mesons. Near the
light-cone, the next-to-leading order QCD corrections for the
vacuum-to-vector-meson correlation function are included at leading power in
$\delta_V = m_V/m_Q$ ($Q=b,c$) within the framework of hard-collinear
factorization. The higher-twist corrections from two-particle and
three-particle vector meson LCDAs are systematically incorporated at leading
order in $\alpha_s$ by applying the method of background field in LCSRs. Based
on these improvements, we perform a systematic computation of the strong
coupling constants $g_{H HV}$ and extract the effective coupling $\beta$ of the
heavy meson chiral perturbation theory (HM$\chi$PT). Furthermore, we accomplish
the analysis for the relation between the coupling $g_{HHV}$ and the residue of
the $H\to V$ transition form factor $A_0$ at heavy pseudoscalar pole.
Additionally, we provide a detailed investigation of the $SU(3)$ flavour
symmetry breaking effects and conduct a comparative analysis with results from
previous studies.
