Based on electron positron collision data collected with the BESIII detector operating at the BEPCII storage rings, the differential cross sections of inclusive π^{0} and K_{S}^{0} production as a function of hadron momentum, normalized by the total cross section of the e^{+}e^{-}→hadrons process, are measured at six center-of-mass energies from 2.2324 to 3.6710 GeV. Our results, which cover a relative hadron energy range from 0.1 to 0.9, significantly deviate from several theoretical calculations based on existing fragmentation functions.