Relativistic jets from accreting supermassive black holes at cosmological distances can be powerful emitters of γ-rays. However, the precise mechanisms and locations responsible for the dissipation of energy within these jets, leading to observable γ-ray radiation, remain elusive. We detect evidence for an intrinsic absorption feature in the γ-ray spectrum at energies exceeding 10 GeV, presumably due to the photon–photon pair production of γ-rays with low-ionization lines at the outer edge of broad-line region (BLR), during the high-flux state of the flat-spectrum radio quasar PKS 1424−418. The feature can be discriminated from the turnover at higher energies resulting from γ-ray absorption in the extragalactic background light. It is absent in the low-flux states, supporting the interpretation that powerful dissipation events within or at the edge of the BLR evolve into fainter γ-ray emitting zones outside the BLR, possibly associated with the moving very long baseline interferometry radio knots. The inferred location of the γ-ray emission zone is consistent with the observed variability timescale of the brightest flare, provided that the flare is attributed to external Compton scattering with BLR photons.