  We suggest an explanation for and explore the consequences of the excess
around 95 GeV in the di-photon and di-tau invariant mass distributions recently
reported by the CMS collaboration at the Large Hadron Collider (LHC), together
with the discrepancy that has long been observed at the Large Electron-Positron
(LEP) collider in the $b\bar b$ invariant mass. Interestingly, the most recent
findings announced by the ATLAS collaboration do not contradict, or even
support, these intriguing observations. Their search in the di-photon final
state similarly reveals an excess of events within the same mass range, albeit
with a bit lower significance, thereby corroborating and somewhat reinforcing
the observations made by CMS. We demonstrate that the lightest CP-even Higgs
boson in the general 2-Higgs Doublet Model (2HDM) Type-III can explain
simultaneously the observed excesses at approximately 1.3 $\sigma$ C.L. while
satisfying up-to-date theoretical and experimental constraints. Moreover, the
2HDM Type-III predicts an excess in the $pp\to t\bar t H_{\rm SM}$ production
channel of the 125 GeV Higgs boson, $H_{\rm SM}$. This effect is caused by a up
to 12\% enhancement of the $H_{\rm SM}tt$ Yukawa coupling in comparison to that
predicted by the Standard Model. Such an effect can be tested at the High
Luminosity LHC (HL-LHC), which can either discover or exclude the scenario we
suggest. This unique characteristic of the 2HDM Type-III makes this scenario
with the 95 GeV resonance very attractive for further theoretical and
experimental investigations at the (HL-)LHC and future colliders.
