  The addition of $SU(2)_L$ triplet fermions of zero hypercharge with the
Standard Model (SM) helps to explain the origin of the neutrino mass by the
so-called seesaw mechanism. Such a scenario is commonly know as the type-III
seesaw model. After the electroweak symmetry breaking the mixings between the
light and heavy mass eigenstates of the neutral leptons are developed which
play important roles in the study of the charged and neutral multiplets of the
triplet fermions at the colliders. In this article we study such interactions
to produce these multiplets of the triplet fermion at the electron-positron and
electron-proton colliders at different center of mass energies. We focus on the
heavy triplets, for example, having mass in the TeV scale so that their decay
products including the SM the gauge bosons or Higgs boson can be sufficiently
boosted, leading to a fat jet. Hence we probe the mixing between light-heavy
mass eigenstates of the neutrinos and compare the results with the bounds
obtained by the electroweak precision study.
