  The study aims to investigate the observability of pseudoscalar Higgs boson
$A$ and neutral heavy CP even Higgs boson $H$, at different benchmark points,
in the framework of type-I 2HDM. The study is done for $e^{-}e^{+}$ collisions
at $\sqrt{s}$ = 1000 GeV centre of mass energy (c.o.m.) a possible scenario in
future lepton collider. The associated production of $A$ and $H$ in $e+ e-$
collisions are investigated in fully hadronic final state in two different
channels. The first one is $AH \to ZHH \to j\bar{j} b \bar{b}b\bar{b}$ while
the other one is $AH \to b \bar{b}b\bar{b}$. The observability of neutral heavy
Higgs and pseudoscalar Higgs signal is possible within the parameter space $
(\tan \beta, m_{A}) $ which satisfies all experimental and theoretical
constraints. The CP odd and CP even Higgs bosons in all scenarios are
observable when signal exceeds $ 5\sigma $, which is the final extracted value
of signal significance. The signal significance is calculated at different
integrated luminosities. It is concluded from current analysis that fully
hadronic channel is promising for search and measurement of the neutral Higgs
Bosons in 2HDM.
