  We analyse in a model independent way the possibilities of digging out
neutral exotic Higgs states, should they exist endowed with unconventional
couplings with ordinary matter and gauge fields, at the 14 TeV run of the Large
Hadron Collider (LHC), adding some comparative studies for 13.6 and 13 TeV
runs. Flavor models, based on some discrete symmetry groups, with extended
scalar sectors are known to yield exotic spin-0 states, both CP-even and
CP-odd, with purely flavor off-diagonal Yukawa couplings. The gauge interaction
of one such CP-even state is also unusual that, unlike the Standard Model Higgs
boson, it does not couple to gauge boson pairs. Such unconventional properties
immune these exotic states from receiving traditional collider and electroweak
constraints, and hence those states could be light. Without committing to any
specific model, exploiting their peculiar Yukawa and gauge properties, we
explore the discovery potential of those exotic Higgs states through some
interesting topologies by figuring out some specific kinematic variables that
suppress the backgrounds.
