  Exotic spin-$0$ states with unusual couplings with the gauge and matter
fields of the Standard Model are worth exploring at the CERN LHC. Though our
approach is largely model independent, we take inspiration from flavor models
based on some discrete symmetries which predict a set of a scalar and a
pseudoscalar having purely off-diagonal Yukawa interactions with quarks and
leptons. In a previous paper, some of us explored how to decipher such exotic
scalar and pseudoscalar states whose off-diagonal Yukawa couplings involve
light quarks. In this work we follow a complementary path and focus on the
Yukawa couplings that necessarily involve a top quark. If one such spin-$0$
state is lighter than the top quark, then the rare decay of the latter, on
account of the high yield of the $t\bar t$ events, could provide a potential
hunting ground of those exotic states particularly during the high luminosity
phase of the LHC run. We carry out an exhaustive collider analysis of some
promising signatures of those exotic states using sophisticated Machine
Learning techniques and obtain considerable signal significance.
