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Ionized proximity zones around luminous quasars provide a unique laboratory to characterize the Lyα emission lines from z > 6 galaxies without significant attenuation from the intergalactic medium (IGM). However, Lyα line measurements for galaxies within high-redshift quasars’ proximity zones have been rare so far. Here we present deep spectroscopic observations obtained with the NIRSpec/Micro-Shutter Assembly (MSA) instrument on the James Webb Space Telescope of galaxies in two z > 6 quasar fields. We measure the Lyα line fluxes for 50 galaxies at 6 < z < 7 with UV absolute magnitude M UV < −19 (median M UV = −19.97), among which 15 are located near the luminous quasars, i.e., within Δv < 2500 km s−1. We find that galaxies near the quasars show significant flux blueward of the systemic Lyα wavelength, and have higher Lyα equivalent width compared to galaxies at similar redshifts that are not located within the quasars’ environment. Our result indicates little or no redshift evolution for the Lyα emitter fraction from z ∼ 6.4 to z ∼ 5. Leveraging the low IGM opacity in the quasars’ vicinity, we evaluate the Lyα escape fraction (f esc Ly α) of high-redshift galaxies. Our analysis suggests that galaxies at 〈z〉 ≈ 6.4 have an average f esc Ly α = 0.14 ± 0.04. This value is consistent with reionization models where the Lyman continuum escape fraction is low ( fescLyC ≲ 0.1 ) for luminous galaxies, and where the most luminous galaxies have only a minor contribution to the total ionizing photon budget.