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We consider a flavour conserving two Higgs doublet model that consists of atype I (or X) quark sector and a generalized lepton sector where the Yukawacouplings of the charged leptons to the new scalars are not proportional to thelepton masses. The model, previously proposed to solve both muon and electron$g-2$ anomalies simultaneously, is also capable to accommodate the ATLAS excessin $pp \rightarrow S \rightarrow \tau^{+}\tau^{-}$ with gluon-gluon fusionproduction in the invariant mass range [0.2; 0.6] TeV, including all relevantlow and high energy constraints. The excess is reproduced taking into accountthe new contributions from the scalar H, the pseudoscalar A, or both. Inparticular, detailed numerical analyses favoured the solution with asignificant hierarchy among the vevs of the two Higgs doublets, $t_{\beta} \sim10$, and light neutral scalars satisfying $m_\mathrm{A} > m_\mathrm{H}$ withsizable couplings to $\tau$ leptons. In this region of the parameter space, themuon $g-2$ anomaly receives one and two loop (Barr-Zee) contributions ofsimilar size, while the electron anomaly is explained at two loops. Ananalogous ATLAS excess in $b$-associated production and the CMS excess in ditopproduction are also studied. Further New Physics prospects concerning theanomalous magnetic moment of the $\tau$ lepton and the implications of the CDF$M_W$ measurement on the final results are discussed.

New Physics hints from $\tau$ scalar interactions and $(g-2)_{e,\mu}$