The Collider Detector at Fermilab (CDF) experiment performed the first measurement of the time-evolution of flavor-tagged B(sub s)(sup 0) (yields) J/(psi)(phi) decays, which probes mixing-induced CP-violation in the B(sub s)(sup 0) sector. Any sizable deviation from zero of the phase (beta)(sub s)J/(psi)(phi), accessible through interference of the (bar b) (yields) (bar c)c(bar s) quark-level process accompanied or not by B(sub s)(sup 0)-(bar B0)sub s (sup 0) mixing, would be unambiguous indication of physics beyond the Standard Model. I report CDF results obtained in 1.35 fb(sup -1), a recent extension to a larger dataset corresponding to 2.8 fb(sup -1), and future projections.