We present a transit-timing variation (TTV) and planetary atmosphere analysis of the Neptune-mass planet HAT-P-26 b. We present a new set of 13 transit light curves from optical ground-based observations and combine them with light curves from the Wide Field Camera 3 on the Hubble Space Telescope, the Transiting Exoplanet Survey Satellite, and previously published ground-based data. We refine the planetary parameters of HAT-P-26 b and undertake a TTV analysis using 33 transits obtained over seven years. The TTV analysis shows an amplitude signal of 1.98 ± 0.05 minutes, which could result from the presence of an additional ~0.02 M Jup planet at a 1:2 mean-motion resonance orbit. Using a combination of transit depths spanning optical to near-infrared wavelengths, we find that the atmosphere of HAT-P-26 b contains ${2.4}_{-1.6}^{+2.9}$ % H2O with a derived temperature of ${590}_{-50}^{+60}$ K.