  Although recent experimental results in b-->s penguin process seem to be
roughly consistent with the standard model predictions, there may be still
large possibilities of new physics hiding in this processes. Therefore, here we
investigate systematically the potential new physics effects that may appear in
time-dependent CP asymmetries of B --> phi K^0, B--> eta^\prime K^0 and B-->
K^0 \pi^0 decay modes, by classifying the cases for the values of the
mixing-induced indirect CP asymmetries, S_{phi K^0}, S_{eta^\prime K^0}, S_{K^0
pi^0} which are compared to S_{J/psi K^0}. We also show that several B_s decay
modes may help to resolve the ambiguities in such an analysis. Through
combining analysis with the time-dependent CP asymmetries of B_s decay modes
such as B_s --> phi eta^\prime, B_s--> eta^\prime pi^0 and B_s --> K^0
bar{K}^0, we can determine where the new CP phases precisely come from.
