  The one-dimensional $p$-wave superconductor, characterized by boundary
Majorana modes, has attracted significant interest owing to its potential
application in topological quantum computation. Similarly, spin-1/2 Kitaev
ladder systems with bond-dependent Ising interactions, featuring Majorana
fermions coupled with $Z_2$ flux, exhibit boundary Majorana modes when in a
topological phase. However, the ground state degeneracy, inherent in these
systems, may result in the annihilation of Majorana modes due to the
superposition of the two states. To address this issue, we introduce a
projective measurement that selects one of the degenerate $Z_2$ sectors,
enabling the emergence of Majorana modes. Once the state is selected, we show
that the application of the local spin operators on a bond flips the sign of
the adjacent $Z_2$ flux. Repeating such operators enables the system to reach a
desired $Z_2$ flux configuration. We present the phase diagram and the
appearance of Majorana modes at the interfaces of topological and
non-topological phases. These modes, along with boundary Majorana modes, can be
manipulated and fused by tuning the flux sectors achievable through applying
local spin operators. We also discuss the engineering of the Kitaev ladder and
open questions for future studies.
