  We present the new and updated $BABAR$ measurements of CP-violation studies
for many $b\to s $ penguin decay modes. We report the first observation of
mixing-induced CP-violation in $B^0 \to \eta ^{'} K^0$ with a significance
(including systematic uncertainties) of 5.5$\sigma$. We also present the first
observation of the decay $B^0 \to \rho ^0 K^0$. Using the time-dependent Dalitz
plot analysis of $B^0\to K^+K^- K^0$ decay, the CP-parameters $\mathcal A_{CP}$
and $\beta_{eff}$ are measured with $4.8\sigma$ significance, and we reject the
solution near $\pi /2 - \beta_{eff}$ at $4.5\sigma$. We also present the
updated measurements of CP-violating parameters for $B^0 \to K_S^0 \pi ^0$,
$K_S^0K_S^0K_S^0$ and $\pi ^0 \pi ^0 K_S^0$ decays. An updated measurements of
the CP-violating charge asymmetries for $B^{\pm}\to \eta ^{'} K^{\pm}$, $\eta
K^{\pm}$, $\omega K^{\pm}$ decays are also presented. The measurements are
based on the data sample recorded at the $\Upsilon (4S)$ resonance with $BABAR$
detector at the PEP-II $B$-meson Factory at SLAC.
