We present an improved measurement of CP-violation parameters in B0-->phiK(0)(S), K(+)K(-)K(0)(S), and eta(')K(0)(S) decays based on a 140 fb(-1) data sample collected at the Upsilon(4S) resonance with the Belle detector at the KEKB energy-asymmetric e(+)e(-) collider. One neutral B meson is fully reconstructed in one of the specified decay channels, and the flavor of the accompanying B meson is identified from its decay products. CP-violation parameters for each of the three modes are obtained from the asymmetries in the distributions of the proper-time intervals between the two B decays. We find that the observed CP asymmetry in the B-->phiK(0)(S) decay differs from the standard model (SM) expectation by 3.5 standard deviations, while the other cases are consistent with the SM.