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  1. The HAWC Collaboration released the 2HWC catalogue of TeV sources, in which 19 show no association with any known high-energy (HE; E ≳ 10 GeV) or very-high-energy (VHE; E ≳ 300 GeV) sources. This catalogue motivated follow-up studies by both the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) and Fermi-LAT (Large Area Telescope) observatories with the aim of investigating gamma-ray emission over a broad energy band. In this paper, we report the results from the first joint work between High Altitude Water Cherenkov (HAWC), MAGIC, and Fermi-LAT on three unassociated HAWC sources: 2HWC J2006+341, 2HWC J1907+084*, and 2HWC J1852+013*. Although no significant detection was found in the HE and VHE regimes, this investigation shows that a minimum 1° extension (at 95 per cent confidence level) and harder spectrum in the GeV than the one extrapolated from HAWC results are required in the case of 2HWC J1852+013*, whilst a simply minimum extension of 0.16° (at 95 per cent confidence level) can already explain the scenario proposed by HAWC for the remaining sources. Moreover, the hypothesis that these sources are pulsar wind nebulae is also investigated in detail.