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 Heiλ10830 near-infrared (NIR) emission. Here we present deep Subaru NIR spectroscopy and He/H determinations for 10 EMPGs, combining the existing optical data and 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 = 0.2379 +0.0031 −0.0030 by linear regression in the (He/H) − (O/H) plane, where our observations increase the number of EMPGs from 3 to 13 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 constraints, we estimate the effective number of neutrino species to be N eff = 2.41 +0.19 −0.21 showing a 2σ tension with the Standard Model value (N eff = 3.046), which may be a hint of an asymmetry in electron-neutrino ν e and antielectron neutrino νe . Allowing the degeneracy parameter of electron-neutrino ξ e to vary as well as N eff and the baryon-to-photon ratio η, we obtain ξ e = 0.05 +0.03 −0.03 , N eff = 3.22 +0.33 −0.30 , and η × 10 10 = 6.13 +0.04 −0.04 from the Y P and D P measurements with a prior of η taken from Planck Collaboration et al. (2020). Our constraints suggest a ν e − νe asymmetry and allow for a high value of N eff within the 1σ level, which could mitigate the Hubble tension.