Quantum criticality plays an important role in the unconventional nature of superconductivity in strongly correlated electron systems. However, the intrinsic antiferromagnetic (AFM) order parameter responsible for quantum criticality has been unidentified in the prototypical unconventional superconductor CeCoIn5. In this work, magnetization and specific-heat measurements for CeCo(In1-xZnx)5 with x≤0.07 demonstrate that the field-induced AFM order develops with Zn doping, along with a continuous increase in its critical field up to 10 T at x=0.07. The weak signals associated with the AFM phase transition strongly suggest spatially inhomogeneous evolution of the AFM phase, whose feature becomes pronounced with decreasing the Zn concentration. The temperature, magnetic field, and Zn concentration phase diagram is constructed from those experimental results. It is found that, in this diagram, extrapolating the x dependence of the AFM critical field yields the value of ≈5T for x→0, which coincides with the location of the quantum critical point in CeCoIn5. The specific heat shows -lnT diverging behavior characteristic of the non-Fermi-liquid state at the AFM critical fields for all of the x range. The scaling analysis for the specific-heat data above critical fields leads to continuous variations of the scaling parameters as a function of x. These findings provide strong evidence that the quantum critical fluctuations in CeCoIn5 originate from the order parameter corresponding to the field-induced AFM state observed in Zn-doped systems.