  In this paper, we examine the consistency of the Large Hadron Collider (LHC)
data collected during Run 1 and 2 by the ATLAS and CMS experiments with the
predictions of a 2-Higgs Doublet Model (2HDM) embedding Vector-Like Quarks
(VLQs) for $pp \to H,A$ production and $H,A\to\gamma\gamma$ decay mechanisms,
respectively, of (nearly) degenerate CP-even ($H$) and CP-odd ($A$) Higgs
bosons. We show that a scenario containing one single VLQ with Electro-Magnetic
(EM) charge $2/3$ can explain the above ATLAS and CMS data for masses in the
region 350 GeV $\leq m_{\rm VLQ}\leq 1.5$ TeV or so, depending on $\tan\beta$,
and for several values of the mixing angle between the top quark ($t$) and its
VLQ counterpart ($T$).We then perform a global fit onto the model by including
all relevant experimental as well as theoretical constraints. The surviving
samples of our analysis are discussed within 2$\sigma$ of the LHC measurements.
Additionally, we also comment on the recent anomalous result reported by CMS
using Run 2 data on the associated Standard Model (SM) Higgs boson production
with top quark pairs $pp\to t\bar th$ with an observed significance of
3.3$\sigma$. Other than these specific examples, we also present a
phenomenological analysis of the main features of the model, including the most
promising $T$ decay channels.
