Fermi-LAT unidentified sources (unIDs) have proven to be compelling targets for performing indirect dark matter (DM) searches. In a previous work, we found that among the 1235 unIDs in Fermi-LAT catalogs (3FGL, 2FHL and 3FHL) only 44 of those are DM subhalos candidates. We now implement a spectral analysis to test whether these remaining sources are compatible or not with DM origin. This analysis is executed using almost 10 years of Pass 8 Fermi-LAT data. None of the unIDs are found to significantly prefer DM-induced emission compared to other, more conventional, astrophysical sources. In order to discriminate between pulsar and DM sources, we developed a new method which is based on the sources spectral curvature, peak energy, and its detection significance. We also look for spatial extension, which may be a hint for a DM origin according to our N-body simulation studies of the subhalo population. In addition, we used Gaia DR2 data to search for a potential stellar counterpart to our best DM subhalo candidates and, although no firm associations could be found, one of them coincides with the Sagittarius stream. Finally, previous constraints on the DM annihilation cross section are updated with the new number of remaining DM subhalo candidates among unIDs. Our limits now rule out canonical thermal WIMPs up to masses of 10 GeV for $bbar{b}$ and 20 GeV for $tau^+tau^-$ annihilation channels, in this way being as sensitive and complementary to those obtained from other targets and probes.
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