We present an improved measurement of CP-violation parameters in B(0)-->phiK(S)(0), K(+)K(-)K(S)(0), and eta(')K(S)(0) decays based on a 140 fb(-1) data sample collected at the Y(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(S)(0) decay differs from the standard model (SM) expectation by 3.5 standard deviations, while the other cases are consistent with the SM.