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Three searches are presented for signatures of physics beyond the standard model (SM) inττfinal states in proton-proton collisions at the LHC, using a data sample collected with the CMS detector at$$ \sqrt{s} $$$\sqrt{s}$= 13 TeV, corresponding to an integrated luminosity of 138 fb⁻¹. Upper limits at 95% confidence level (CL) are set on the products of the branching fraction for the decay intoτleptons and the cross sections for the production of a new bosonϕ, in addition to the H(125) boson, via gluon fusion (ggϕ) or in association with b quarks, ranging from$$ \mathcal{O} $$$O$(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 ggϕproduction with localp-values equivalent to about three standard deviations atm_ϕ= 0.1 and 1.2 TeV. In a search fort-channel exchange of a vector leptoquark U₁, 95% CL upper limits are set on the dimensionless U₁leptoquark coupling to quarks andτleptons 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$$ {M}_{\textrm{h}}^{125} $$$M_h^{125}$and$$ {M}_{\textrm{h},\textrm{EFT}}^{125} $$$M_{h,\mathrm{EFT}}^{125}$minimal supersymmetric SM benchmark scenarios, additional Higgs bosons with masses below 350 GeV are excluded at 95% CL.