This paper presents the results from point-like neutrino source searches using ten years of IceCube data collected between Apr.~6, 2008 and Jul.~10, 2018. We evaluate the significance of an astrophysical signal from a point-like source looking for an excess of clustered neutrino events with energies typically above $sim1,$TeV among the background of atmospheric muons and neutrinos. We perform a full-sky scan, a search within a selected source catalog, a catalog population study, and three stacked Galactic catalog searches. The most significant point in the Northern hemisphere from scanning the sky is coincident with the Seyfert II galaxy NGC 1068, which was included in the source catalog search. The excess at the coordinates of NGC 1068 is inconsistent with background expectations at the level of $2.9,sigma$ after accounting for statistical trials. The combination of this result along with excesses observed at the coordinates of three other sources, including TXS 0506+056, suggests that, collectively, correlations with sources in the Northern catalog are inconsistent with background at 3.3$,sigma$ significance. These results, all based on searches for a cumulative neutrino signal integrated over the ten years of available data, motivate further study of these and similar sources, including time-dependent analyses, multimessenger correlations, and the possibility of stronger evidence with coming upgrades to the detector.
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