A bstract 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 $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 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 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 (gg ϕ ) or in association with b quarks, ranging from $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> (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 gg ϕ production with local p -values equivalent to about three standard deviations at m ϕ = 0 . 1 and 1.2 TeV. In a search for t -channel exchange of a vector leptoquark U 1 , 95% CL upper limits are set on the dimensionless U 1 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 $$ {M}_{\textrm{h}}^{125} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>h</mml:mi> <mml:mn>125</mml:mn> </mml:msubsup> </mml:math> and $$ {M}_{\textrm{h},\textrm{EFT}}^{125} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>,</mml:mo> <mml:mi>EFT</mml:mi> </mml:mrow> <mml:mn>125</mml:mn> </mml:msubsup> </mml:math> minimal supersymmetric SM benchmark scenarios, additional Higgs bosons with masses below 350 GeV are excluded at 95% CL.