Abstract
The mixing induced time dependent CP asymmetry, direct CP asymmetry, and branching ratio in $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}{K}_{S}$ in a model III two Higgs doublet model are calculated, in particular, neutral Higgs boson contributions are included. It is shown that satisfying all the relevant experimental constraints, for time dependent CP asymmetry ${S}_{\ensuremath{\varphi}K}$ model III can agree with the present data, ${S}_{\ensuremath{\varphi}k}=\ensuremath{-}0.39\ifmmode\pm\else\textpm\fi{}0.41,$ within a $1\ensuremath{\sigma}$ error, and the direct CP asymmetry which is zero in the SM can be about $\ensuremath{-}8%$ to $\ensuremath{-}20%$ in the reasonable regions of the parameters.
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