The primordial He abundance Y _P is a powerful probe of cosmology. Currently, Y _P is best determined by observations of metal-poor galaxies, while there are only a few known local extremely metal-poor (<0.1Z _⊙) galaxies (EMPGs) having reliable He/H measurements with He i λ10830 near-infrared (NIR) emission. Here we present deep Subaru NIR spectroscopy for 10 EMPGs. Combining the existing optical data, He/H values of 5 out of the 10 EMPGs are reliably derived by the Markov chain Monte Carlo algorithm. Adding the existing 3 EMPGs and 51 moderately metal-poor (0.1-0.4Z _⊙) galaxies with reliable He/H estimates, we obtain Y P = 0.2370 − 0.0034 + 0.0033 by linear regression in the (He/H) − (O/H) plane, where we increase the number of EMPGs from three to eight anchoring He/H of the most metal-poor gas in galaxies. Although our Y _P measurement and previous measurements are consistent, our result is slightly (∼1σ) smaller due to our EMPGs. Including the existing primordial deuterium D _P measurement, we constrain the effective number of neutrino species N _eff and the baryon-to-photon ratio η showing ≳1-2σ tensions with the Standard Model and Planck Collaboration et al. (2020). Motivated by the tensions, we allow the degeneracy parameter of the electron neutrino ξ _e , as well as N _eff and η, to vary. We obtain ξ e = 0.05 − 0.02 + 0.03 , N eff = 3.11 − 0.31 + 0.34 , and η × 10 10 = 6.08 − 0.06 + 0.06 from the Y _P and D _P measurements with a prior of η taken from Planck Collaboration et al. Our constraints suggest a lepton asymmetry and allow for a high value of N _eff within the 1σ level, which could mitigate the Hubble tension.