Binary systems are a well-established subclass of gamma-ray sources. The high mass X-ray binary pulsar 1A 0535+262 has been considered to be a possible gamma-ray emitter for a long time, although former gamma-ray searches using the Fermi Large Area Telescope (LAT) and VERITAS data resulted in upper limits only. We aim at a deep search for gamma-ray emission and pulsations from 1A 0535+262 using more than 13 yr of Fermi-LAT data. The analysis was performed for both the whole Fermi-LAT data set, as well as for the X-ray outbursts that 1A 0535+262 has experienced since the launch of Fermi. Various X-ray observations have been used to generate the ephemeris for the pulsation search. We also investigate the long-term gamma-ray flux variability and perform orbital phase-resolved analysis for the outbursts. We did not detect any steady or pulsed gamma-ray emission from 1A 0535+262 during the whole Fermi-LAT mission span or its X-ray outbursts. We thus derived the deepest gamma-ray luminosity upper limits to date at the 95% confidence level to be around (2.3-4.7) x 10(32) erg s(-1) depending on different spectral indices assumed, which results in a ratio of L ( gamma ) to L (X) (2-150 keV) being (1.9-3.9) x 10(-6).