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The Large High Altitude Air Shower Observatory (LHAASO) has detected multipleultra-high energy (UHE; E$_\gamma \ge$ 100 TeV) gamma-ray sources in the MilkyWay Galaxy, which are associated with Galactic ``PeVatrons'' that accelerateparticles up to PeV (= 10$^{15}$ eV) energies. Although supernova remnants(SNRs) and pulsar wind nebulae (PWNe), as source classes, are considered theleading candidates, further theoretical and observational efforts are needed tofind conclusive proof to confirm the nature of these PeVatrons. This work aimsto provide a phenomenological model to account for the emission observed fromthe direction of LHAASO J0341+5258, an unidentified UHE gamma-ray sourceobserved by LHAASO. 15 years of Fermi-LAT data was analyzed to find the highenergy (HE; 100 MeV $\le$ E$_\gamma$ $\le$ 100 GeV) GeV gamma-ray counterpartof LHAASO J0341+5258, in the 4FGL-DR3 catalog. We have explained the spectrumof the closest 4FGL source, 4FGL J0340.4+5302, by a synchro-curvature emissionformalism typically used in the case of GeV pulsars. Escape-limited hadronicinteraction between protons accelerated in an old, now invisible SNR and coldprotons inside associated molecular clouds (MCs) and leptonic emission from aputative TeV halo was explored to explain the multi-wavelength (MWL) spectralenergy distribution (SED) observed from the LHAASO source region. We havefurther discussed possible observational avenues that can be explored in thenear future and predicted the outcome of those observational efforts from themodel explored in this paper.

Dissecting the emission from LHAASO J0341+5258: implications for future multi-wavelength observations