A fundamental problem posed from the study of correlated electron compounds, of which heavy-fermion systems are prototypes, is the need to understand the physics of states near a quantum critical point (QCP). At a QCP, magnetic order is suppressed continuously to zero temperature and unconventional superconductivity often appears. Here, we report pressure (P)-dependent 115 In nuclear quadrupole resonance (NQR) measurements on heavy-fermion antiferromagnet CeRh 0.5 Ir 0.5 In 5. These experiments reveal an antiferromagnetic (AF) QCP at P AF c ¼ 1:2 GPa where a dome of superconductivity reaches a maximum transition temperature T c. Preceding P AF c , however, the NQR frequency ν Q undergoes an abrupt increase at P Ã c = 0.8 GPa in the zero-temperature limit, indicating a change from localized to itinerant character of cerium's f-electron and associated small-to-large change in the Fermi surface. At P AF c where T c is optimized, there is an unusually large fraction of gapless excitations well below T c that implicates spin-singlet, odd-frequency pairing symmetry.