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Abstract Single crystals of the quasi-skutterudite compounds Ca₃(Ir_1-xRh_x)₄Sn₁₃(3–4–13) were synthesized by flux growth and characterized by x-ray diffraction, energy dispersive x-ray spectroscopy, magnetization, resistivity, and radio frequency magnetic susceptibility techniques. The coexistence and competition between the charge density wave (CDW) and superconductivity was studied by varying the Rh/Ir ratio. The superconducting transition temperature, $T_{\mathrm{c}}$, varies from 7 K in pure Ir (x = 0) to 8.3 K in pure Rh (x = 1). Temperature-dependent electrical resistivity reveals monotonic suppression of the CDW transition temperature,T_CDW(x). The CDW starts in pure Ir,x = 0, atT_CDW≈ 40 K and extrapolates roughly linearly to zero at $x_c\approx$0.53–0.58 under the superconducting dome. Magnetization and transport measurements show a significant influence of CDW on superconducting and normal states. Meissner expulsion is substantially reduced in the CDW region, indicating competition between the CDW and superconductivity. The low-temperature resistivity is higher in the CDW part of the phase diagram, consistent with the reduced density of states due to CDW gapping. Its temperature dependence just above $T_{\mathrm{c}}$shows signs of non-Fermi liquid behavior in a cone-like composition pattern. We conclude that the Ca₃(Ir_1-xRh_x)₄Sn₁₃alloy is a good candidate for a composition-driven quantum critical point at ambient pressure.