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 bb¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\\overline{b} $$\\end{document}, even being fermiophobic, the 4b + W state via pp → H±A → (AW)A → 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 tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document}+jets background and hence constructing a suitable discriminator based on the signal hypothesis and signal topology is necessary. We devised a χ2 variable as the most suitable signal-background discrimintor to reduce the background by a sizable amount and showed the discovery reach (> 3σ) of the electroweak initiated final state at the LHC.