In many classes of unconventional superconductors, the question of whether the superconductivity is enhanced by the quantum-critical fluctuations on the verge of an ordered phase remains elusive. One of the most direct ways of addressing this issue is to investigate how the superconducting dome traces a shift of the ordered phase. Here, we study how the phase diagram of the iron-based superconductor BaFe 2 (As 1−x P x ) 2 changes with disorder via electron irradiation, which keeps the carrier concentrations intact. With increasing disorder, we find that the magneto-structural transition is suppressed, indicating that the critical concentration is shifted to the lower side. Although the superconducting transition temperature T c is depressed at high concentrations (x 0.28), it shows an initial increase at lower x. This implies that the superconducting dome tracks the shift of the antiferromagnetic phase, supporting the view of the crucial role played by quantum-critical fluctuations in enhancing superconductivity in this iron-based high-T c family.In strongly correlated electron systems such as heavy fermions, cuprates, and organic materials, superconductivity often emerges when the antiferromagnetic (AFM) order is suppressed through control parameters such as pressure and chemical composition. 1,2) A striking feature in these materials is that, in several cases, physical properties that deviate from the conventional Fermi-liquid theory (i.e., non-Fermi liquid properties) also appear when the AFM transition is tuned to zero temperature (T ), suggesting the existence of an AFM quantum critical point (QCP). Although it is widely believed that quantum-critical fluctuations originating from the QCP are closely related to the superconductivity through unconventional pairing mechanisms, 3,4) it remains unclear whether the QCP actually exists inside the superconducting dome. The recently discovered iron pnictides 5) also exhibit superconductivity in the vicinity of AFM order accompanying tetragonal-to-orthorhombic structural transitions. 6) These magneto-structural transitions can be suppressed by pressure or chemical substitution, 7) but the quantum criticality is often avoided by a first-order transition in several systems. 6) Among the iron pnictides, Phosphorus(P)-substituted BaFe 2 As 2 is a particularly clean system, and moreover, is unique in the fact that there is growing evidence for the existence of a QCP inside the superconducting dome near the optimal composition. 8-13) Although a QCP located at the maximum T c naturally leads to the consideration that the quantum-critical fluctuations help to enhance superconductivity, there has been no direct evidence against a scenario that it is just a coincidence. A direct test to address this issue is to investigate how the superconducting dome traces when the AFM phase is shifted. However, it has been quite challenging to perform such experiments without changing the carrier numbers or bandwidth, whose effects on the QCP and superconductivity are nontrivial. In fact, ...