One of the greatest challenges to Landau's Fermi liquid theory - the standard theory of metals - is presented by complex materials with strong electronic correlations. In these materials, non-Fermi liquid transport and thermodynamic properties are often explained by the presence of a continuous quantum phase transition which happens at a quantum critical point (QCP). A QCP can be revealed by applying pressure, magnetic field, or changing the chemical composition. In the heavy-fermion compound CeCoIn5, the QCP is assumed to play a decisive role in defining the microscopic structure of both normal and superconducting states. However, the question of whether QCP must be present in the material's phase diagram to induce non-Fermi liquid behavior and trigger superconductivity remains open. Here we show that the full suppression of the field-induced QCP in CeCoIn5 by doping with more than 20% Yb on the Ce site has surprisingly little impact on both unconventional superconductivity and non-Fermi liquid behavior. This implies that the non-Fermi liquid metallic behavior for large Yb doping could be a new state of matter in its own right rather than a consequence of the underlying quantum phase transition.