  Majorana zero modes are well studied in the gapped phases of topological
systems. We investigate Majorana zero modes at the topological quantum
criticality in one dimensional topological superconducting model with longer
range interaction. We identify stable localized Majorana zero modes appearing
at criticality under certain conditions. Topological invariant number for these
non-trivial criticalities is obtained from zeros of a complex function
associated with the Hamiltonian. Behavior of parametric curve at criticalities
validate the invariant obtained and account for the appearance of Majorana zero
modes at criticality. Trivial and non-trivial topological nature of criticality
due to the presence of multicritical point cause an unusual topological
transition along the critical line. We observe and investigate this unique
transition in terms of eigenvalue spectrum. Appearance of MZMs at criticality
demands integer value of topological invariant number in order to validate the
concept of bulk-boundary correspondence. Hence we propose a scheme to separate
the invariant number into fractional and integer contribution to establish
bulk-boundary correspondence at criticality.
