  The weak decays of B_{c} --> D_{s}^{*}l^{+}l^{-} (l=mu,tau) are investigated
in the Standard Model with fourth generation (SM4). Taking fourth generation
quark mass m_{t'} of about 300 to 600 GeV with the CKM matrix elements
V_{t'b}^{*}V_{t's} in the range (0.03-1.2)*10^{-2} and using the new CP odd
phase (phi_{sb}) to be 90^{o} the analysis of decay rates, forward-backward
asymmetries, lepton polarization asymmetries and the helicity fractions of
D_{s}^{*} meson in B_{c} --> D_{s}^{*}l^{+}l^{-} (l=mu,tau) is made. It is
shown that the values of these physical observables are greatly influenced by
the effects of extra sequential quark generation in the SM. It is found that
the zero position of the forward-backward asymmetry in B_{c} --> D_{s}^{*}
mu^{+} mu^{-} deviates significantly from that of the SM value while the
effects in the decay rate, helicity fractions of D_s^{*} meson and the lepton
polarization asymmetries are also quite promising. In B_{c} --> D_{s}^{*}
tau^{+} tau^{-} decay, the SM4 the NP effects are somewhat mild in the decay
rate and forward-backward asymmetry but they have shown them up in the
longitudinal and transverse lepton polarization and also in the helicity
fractions of the D_{s}^{*} meson which differ distinctively from the SM values.
Thus the study of these physical observables will provide us useful information
to probe new physics and helps us to search for the fourth generation of quarks
(t',b') in an indirect way.
