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Recently, the region surrounding eHWC J1842−035 has been studied extensively by γ-ray observatories due to its extended emission reaching up to a few hundred TeV and potential as a hadronic accelerator. In this work, we use 1910 days of cumulative data from the High Altitude Water Cherenkov (HAWC) observatory to carry out a dedicated systematic source search of the eHWC J1842−035 region. During the search, we found three sources in the region, namely, HAWC J1844−034, HAWC J1843−032, and HAWC J1846−025. We have identified HAWC J1844−034 as the extended source that emits photons with energies up to 175 TeV. We compute the spectrum for HAWC J1844−034, and by comparing with the observational results from other experiments, we have identified HESS J1843−033, LHAASO J1843−0338, and TASG J1844−038 as very-high-energy γ-ray sources with a matching origin. Also, we present and use the multiwavelength data to fit the hadronic and leptonic particle spectra. We have identified four pulsar candidates in the nearby region in which PSR J1844−0346 is found to be the most likely candidate due to its proximity to HAWC J1844−034 and the computed energy budget. We have also found SNR G28.6−0.1 as a potential counterpart source of HAWC J1844−034 for which both leptonic and hadronic scenarios are feasible.