  We explore the ground state energies of the neutral and charged vector
$K^{*}$ mesons in the external abelian magnetic field of QCD scale using
overlap fermions. We attempt to calculate the magnetic moment and the magnetic
dipole polarizability of the $K^{*0}$ and $\bar{K}^{*0}$ mesons and investigate
their dependence on the ratio of the strange quark mass to the light quark
mass. It is found that the ground state energy and the magnetic dipole
polarizability depends on the meson spin projection on the magnetic field axis.
This leads to the appearance of dileptonic asymmetry, which can be
characterized by the tensor polarizability estimated for the $K^{*0}$ mesons.
We obtain that the $g$-factor of the vector $K^{*\pm}$ mesons depends on the
$m_s/m_u$ value. Also we do not observe any evidence of the tachyon mode
existence for the strange vector mesons.
