Three searches are presented for signatures of physics beyond the standard model (SM) in ττ final states in proton-proton collisions at the LHC, using a data sample collected with the CMS detector at ss = 13 TeV, corresponding to an integrated luminosity of 138 fb−1−1. Upper limits at 95% confidence level (CL) are set on the products of the branching fraction for the decay into τ leptons and the cross sections for the production of a new boson ϕ, in addition to the H(125) boson, via gluon fusion (ggϕ) or in association with b quarks, ranging from OO(10 pb) for a mass of 60 GeV to 0.3 fb for a mass of 3.5 TeV each. The data reveal two excesses for ggϕ production with local p-values equivalent to about three standard deviations at mϕϕ = 0.1 and 1.2 TeV. In a search for t-channel exchange of a vector leptoquark U11, 95% CL upper limits are set on the dimensionless U11 leptoquark coupling to quarks and τ leptons ranging from 1 for a mass of 1 TeV to 6 for a mass of 5 TeV, depending on the scenario. In the interpretations of the Mh125Mh125 and Mh,EFT125Mh,EFT125 minimal supersymmetric SM benchmark scenarios, additional Higgs bosons with masses below 350 GeV are excluded at 95% CL.