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This paper presents the results from point-like neutrino source searchesusing 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-likesource looking for an excess of clustered neutrino events with energiestypically above $\sim1\,$TeV among the background of atmospheric muons andneutrinos. We perform a full-sky scan, a search within a selected sourcecatalog, a catalog population study, and three stacked Galactic catalogsearches. The most significant point in the Northern hemisphere from scanningthe sky is coincident with the Seyfert II galaxy NGC 1068, which was includedin the source catalog search. The excess at the coordinates of NGC 1068 isinconsistent with background expectations at the level of $2.9\,\sigma$ afteraccounting for statistical trials. The combination of this result along withexcesses observed at the coordinates of three other sources, including TXS0506+056, suggests that, collectively, correlations with sources in theNorthern catalog are inconsistent with background at 3.3$\,\sigma$significance. These results, all based on searches for a cumulative neutrinosignal integrated over the ten years of available data, motivate further studyof these and similar sources, including time-dependent analyses, multimessengercorrelations, and the possibility of stronger evidence with coming upgrades tothe detector.

Time-integrated Neutrino Source Searches with 10 years of IceCube Data