  In this article, we explore the possibility of displaced Higgs production
from the decays of the heavy fermions in the Type-III seesaw extension of the
Standard Model at the LHC/FCC and the muon collider. The displaced heavy
fermions and the Higgs boson can be traced back by measuring the displaced
charged tracks of the charged leptons along with the $b$-jets. A very small
Yukawa coupling can lead to two successive displaced decays which makes the
phenomenology even more interesting. The prospects of the transverse and
longitudinal displaced decay lengths are extensively studied in the context of
the boost at the LHC/FCC. Due to the parton distribution function, the
longitudinal boosts leads to larger displacement compared to the transverse
one, which can reach MATHUSLA and beyond. The longitudinal measurements are
indeed possible by the visible part of the finalstate, which captures the
complete information about the longitudinal momenta. The comparative studies
are made at the LHC/FCC with the centre of mass energies of 14, 27 and 100 TeV,
respectively. A futuristic study of the muon collider where the collision
happen in the centre of mass frame is analysed for centre of mass energies of
3.5, 14 and 30 TeV. Contrary to LHC/FCC, here the transverse momentum diverges,
however, the maximum reach in both the direction are identical due to the
constant total momentum in each collision. The reach of the Yukawa couplings
and fermion masses are appraised for both the colliders. FCC at 100 TeV can
probe a mass of 4.25 TeV and a lowest Yukawa coupling of $\mathcal{O}(5 \times
10^{-11})$.
