We report the light-curve analysis for the event MOA-2020-BLG-135, which leads to the discovery of a new Neptune-class planet, MOA-2020-BLG-135Lb. With a derived mass ratio of $q={1.52}_{-0.31}^{+0.39}\times {10}^{-4}$ and separation s ≍ 1, the planet lies exactly at the break and likely peak of the exoplanet mass-ratio function derived by the Microlensing Observations in Astrophysics (MOA) Collaboration. We estimate the properties of the lens system based on a Galactic model and considering two different Bayesian priors: one assuming that all stars have an equal planet-hosting probability and the other that planets are more likely to orbit more-massive stars. With a uniform host mass prior, we predict that the lens system is likely to be a planet of mass ${m}_{\mathrm{planet}}={11.3}_{-6.9}^{+19.2}{M}_{\oplus }$ and a host star of mass ${M}_{\mathrm{host}}={0.23}_{-0.14}^{+0.39}{M}_{\odot }$ , located at a distance ${D}_{L}={7.9}_{-1.0}^{+1.0}\ \mathrm{kpc}$ . With a prior that holds that planet occurrence scales in proportion to the host-star mass, the estimated lens system properties are ${m}_{\mathrm{planet}}={25}_{-15}^{+22}{M}_{\oplus }$ , ${M}_{\mathrm{host}}={0.53}_{-0.32}^{+0.42}{M}_{\odot }$ , and ${D}_{L}={8.3}_{-1.0}^{+0.9}\ \mathrm{kpc}$ . This planet qualifies for inclusion in the extended MOA-II exoplanet microlens sample.