The Icecube neutrino observatory is a cubic-kilometer particle detector located at the South Pole. A system of public real-time alerts on neutrino candidate events likely to be of astrophysical origin has been operating since 2016. On November 14th, 2020, a track-like event with a high probability of being of astrophysical origin (IC-201114A) was reported. 4FGL~J0658.6+0636, a source of the blazar type, was identified inside the 90\% localisation region of the alert 0.8$^{\circ}$ from the best-fit event position by the Fermi-LAT collaboration. In this work, we analyse 12.3 years of \textit{Fermi}-LAT data from 4FGL~J0658.6+0636. No indication of significant gamma-ray activity was found around the time of the alert, however, two periods in which the source was detected significantly were identified and studied considering a lepto-hadronic scenario. We investigate a possible photohadronic origin for high-energy neutrinos and calculate the gamma-ray contribution to the spectral energy distribution (SED). The predicted neutrino flux and the expected time for a neutrino detection from the source during a flaring state were calculated for the periods of significant activity. Assuming the historical behaviour of the source, an approximation of the gamma-ray and neutrino flux coming from photohadronic interactions around the IC-alert is also given.