Detection of the Extended $\gamma$-ray Emission around TeV source 1LHAASO J0249+6022 with Fermi-LAT
1LHAASO J0249+6022 is an extended very-high-energy gamma-ray source discovered by the Large High-Altitude Air Shower Observatory. Based on nearly 16.1 years of data from the Fermi Large Area Telescope, we report the probable gamma-ray emission from 1LHAASO J0249+6022 in the 0.03-1 TeV energy range. The results show that its gamma-ray spectrum can be well fitted by a single power law with an index of 1.54 $\pm$ 0.17, and integral photon flux is (4.28 $\pm$ 1.03) $\times$ 10$^{-11}$ photons cm$^{-2}$ s$^{-1}$. We also considered theoretically whether the non-thermal emission could originate from a pulsar wind nebula (PWN) scenario. Assuming that the particles injected into the nebula have a power-law distribution, the resulting spectrum from the inverse Compton scattering is consistent with the detected GeV and TeV gamma-ray fluxes. Our study shows that the PWN scenario is reasonable for 1LHAASO J0249+6022.