We conducted an analysis of γ-ray data of TXS 0506+056 detected by Fermi LAT spanning from August 1, 2010, to October 22, 2023. We generated a comprehensive light curve covering the entire thirteen-years period. Through this analysis, we identified potential flaring events within the data and the correlation of the IceCube–170922A neutrino event with the flaring. In 1-day time binning, we determined energy flux, photon flux, and spectral index. The spectral index was at its lowest value of 2.003 ± 0.057, and the average energy flux was at (1.945 ± 0.211) ×10−4 MeV cm−2 s−1 at the detection date of IceCube–170922A neutrino event. This indicates a significant flattening/hardening of the spectrum during the detection of the IceCube–170922A neutrino event.