We report on the identification of a new γ-ray-emitting narrow-line Seyfert 1 galaxy (γ-NLS1), SDSS J095909.51+460014.3 (z = 0.399), by establishing an association with a γ-ray source 4FGL 0959.6+4606, although its low-energy counterpart was suggested to be a radio galaxy (RG) 2MASX J09591976+4603515. Wide-field Infrared Survey Explorer long-term light curves of these two sources reveal diverse infrared variability patterns. Brightenings of 2.5 mag are detected for the former source, while flux decays of 0.5 mag are found for the other one. More importantly, the time that the infrared flux of the NLS1 rises is coincident with the time of flux increase of 4FGL 0959.6+4606. At the same time, no infrared activity of the RG has been observed. A specific analysis of 15-month data from Large Area Telescope aboard Fermi, aimed at the high γ-ray flux state, yields a significant source (TS = 43). The corresponding γ-ray localisation analysis suggests that only the NLS1 falls into the uncertainty area, further supporting the updated association relationship. A broadband spectral energy distribution of SDSS J095909.51+460014.3 has been drawn and well described by the classic single-zone homogeneous leptonic jet model. Its jet properties were investigated and found to be comparable with the known γ-NLS1s.