  Most of the experimental searches of the non-Standard Model Higgs boson(s) at
the LHC rely on the QCD induced production modes. However, in some beyond
Standard Model frameworks, the additional Higgs bosons can have fermiophobic
behaviour. The type I two Higgs doublet model considered here is a perfect
example where all the additional Higgs bosons exhibit fermiophobic nature over
a large region of parameter space. Thus the electroweak productions of these
new Higgs bosons are more dominant over the QCD induced processes. In scenarios
with light pseuodoscalar ($A$) which is bound to decay dominantly to
$b\bar{b}$, even being fermiophobic, the $4b + W$ state via $p p \to H^\pm A
\to (AW)A \to 4b + W$ and followed by the leptonic decay of $W$ boson can
surpass the QCD initiated $4b$ final state. However, the signal gets
overshadowed by large $t\bar{t}+$jets background and hence constructing a
suitable discriminator based on the signal hypothesis and signal topology is
necessary. We devised a $\chi^2$ variable as the most suitable
signal-background discrimintor to reduce the background by a sizable amount and
showed the discovery reach ( $>3\sigma$) of the electroweak initiated $4b+ \ell
+ {\rlap{\,/}{E}_T}$ final state at the LHC.
