  The exclusive semileptonic $B\to K_{1}(1270) \ell^{+}\ell^{-}$ ($\ell=\mu ,
\tau$) decays are analyzed in variants of two Higgs double models (THDMs). The
mass eigenstates $K_{1}(1270)$ and $K_{1}(1400)$ are the mixture of two
axial-vector SU(3) $^{1}{P}_{1}$ and $^{3}{P}_{1}$ states with the mixing angle
$\theta_{K}$. Making use of the form factors calculated in the Light Cone QCD
approach and by taking the mixing angle $\theta_{K}=-34^{\circ}$, the impact of
the parameters of the THDMs on different asymmetries in above mentioned
semileptonic $B$ meson decays are studied. In this context the forward-backward
asymmetry and different lepton polarization asymmetries have been analyzed. We
have found comprehensive effects of the parameters of the THDMs on the above
mentioned asymmetries. Therefore, the precise measurements of these asymmetries
at the LHC and different $B$ factories, for the above mentioned processes, can
serve as a good tool to put some indirect constraints on the parametric space
of the different versions of THDM.
