The low refractive index layers in the mirror coatings of the room-temperature laser interferometer gravitational waves detectors are silica deposited by the ion beam sputter method. However, the silica film suffers from the cryogenic mechanical loss peak, hindering its application for the next generation detector operated at cryogenics. New low refractive index materials need to be explored. We study amorphous silicon oxy-nitride (SiON) films deposited using the method of plasma-enhanced chemical vapor deposition. By changing the N_{2}O/SiH_{4} flow rate ratio, we can tune the refractive index of the SiON smoothly from nitridelike to silicalike of ∼1.48 at 1064 nm, 1550 nm, and 1950 nm. Thermal anneal reduced the refractive index down to ∼1.46 and effectively reduced the absorption and cryogenic mechanical loss; the reductions correlated with the N─H bond concentration decrease. Extinction coefficients of the SiONs at the three wavelengths are reduced down to 5×10^{-6}∼3×10^{-7} by annealing. Cryogenic mechanical losses at 10 K and 20 K (for ET and KAGRA) of the annealed SiONs are significantly lower than the annealed ion beam sputter silica. They are comparable at 120 K (for LIGO-Voyager). Absorption from the vibrational modes of the N─H terminal-hydride structures dominates over the absorption from other terminal hydrides, the Urbach tail, and the silicon dangling bond states in SiON at the three wavelengths.