We show the presence of a quantum critical point in CeRu_2-xCo_xGe₂ (0 ≤ x ≤ 2) using detailed heat capacity and muon spin relaxation (μSR) measurements. The millikelvin heat capacity and μSR results for the critical composition x_C ~ 1. 5 are consistent with the spin fluctuation model of the quantum critical point. The time-field-temperature scaling of the heat capacity and μSR data further suggests the role of critical and cooperative spin fluctuations near the antiferromagnetic quantum critical point. In addition, the temperature-dependent x-ray absorption near edge structure reveals intermediate valence fluctuation down to the lowest temperature for the compositions x ≥ 1.5. The noninteger valence for the critical composition x_C ~ 1.5 is further demonstrated by room temperature x-ray photoelectron spectroscopy. Interestingly, the quantum criticality in CeRu_2-xCo_xGe₂ is governed by the survival of valence and spin fluctuations down to the lowest temperature.