Markarian (Mrk) 180 is a High frequency-peaked BL Lacertae object or HBL object, located at a redshift of 0.045 and a potential candidate for high-energy cosmic ray acceleration. In this work, we have done a temporal and spectral study using Fermi Large Area Telescope (Fermi-LAT) $\gamma$-ray data, collected over 12.8 years. In the case of the temporal study, the 12.8 years long, 30-day binned, Fermi-LAT $\gamma$-ray light curve does not show any significant enhancement of the flux. To understand the underlying physical mechanism, we focused our study on multi-wavelength spectral analysis. We constructed multi-wavelength spectral energy distribution (MWSED) using Swift X-ray, ultraviolet & optical, and X-ray Multi-Mirror Mission (XMM-Newton) data, which have been analysed thoroughly. The SED has been modelled with three different models: (i) pure leptonic scenario and lepto-hadronic scenario where we considered two types of lepto-hadronic interactions (ii) line-of-sight interactions of ultrahigh-energy cosmic rays (UHECR; $E\gtrsim 10^{17}$ eV) with the cosmic background radiation and (iii) interaction between relativistic protons with the cold proton within the blazar jet. In this literature, we have done a detailed comparative study between all these three models. In an earlier study, Mrk 180 was associated with the Telescope Array (TA) hotspot of UHECRs at $E>57$ EeV which motivates us to check whether Mrk 180 can be a source of UHECRs, contributing to the TA hotspot. From our study, we find, for conservative strengths of the extragalactic magnetic field, Mrk 180 is unlikely to be a source of UHECR events.