We demonstrate a magnetic quantum critical point embedded within the superconducting state of Zn-doped CeCoIn₅, revealed by a pronounced peak in the magnetic penetration depth at zero temperature λ(0). Using scanning SQUID microscopy, we determine the local superconducting transition temperature T_c and λ(0). By parameterizing λ(0) in terms of the local T_c rather than nominal Zn substitution, we circumvent the ambiguity caused by doping inhomogeneity and enable a more precise extraction of the critical exponent. The extracted exponent exceeds the clean spin-density-wave value, indicating a disorder-modified quantum critical regime. The enhancement of λ(0) reflects the suppression of the superfluid stiffness and is consistent with critical scaling. Our approach provides a route to uncover intrinsic quantum critical behavior hidden by inhomogeneity in unconventional superconductors.