The supernova remnant (SNR) G150.3+4.5 was first identified in radio, exhibiting a hard GeV spectrum and a ~1.5º radius. Radio observations revealed a bright arc with an index of ~−0.40, which stands in contrast to the index of ~−0.69 for the rest. This arc is coincident with the point-like Fermi source 4FGL J0426.5+5434 and KM2A source 1LHAASO J0428+5531. The rest of the SNR has a hard GeV spectrum and a soft TeV spectrum, implying a spectral cut-off or break near 1 TeV. Since there is no X-ray counterpart and no pulse signal detected, the gamma-ray (γ-ray) emission mechanism from the SNR and the point-like source appear puzzling. In this work, we reanalyse the γ-ray emission using 14 yr data recorded by Fermi Large Area Telescope and find that the spectrum of the northern half-sphere is compatible with a broken power law with a break at 146 ± 11 eV and photon indices of ΓNorthlobe = 1.54 ± 0.04stat ± 0.07syst (2.28 ± 0.08stat ± 0.12syst) below (above) the break. In addition, the southern half-sphere can be described well with a single power law with ΓSouthlobe =1.95 ± 0.07stat ± 0.09syst. Since the southern half-sphere is well correlated with CO emission, we propose that the γ-ray emission of the northern half-sphere could be dominated by relativistic electrons via inverse-Compton processes, while the southern half-sphere is dominated by cosmic rays via hadronic processes. 4FGL J0426.5+5434 may result from the illumination of a cloud by escaping cosmic rays or recent shock-cloud interaction. Observations from LHAASO-KM2A thus favour the possibility of a cosmic-ray PeVatron candidate, however, leptonic scenarios cannot be ruled out. Further multi-wavelength observations are warranted to confirm the hadronic nature of 1LHAASO J4028+5531.