  Recent experiment reported the evidence of dispersing one-dimensional
Majorana mode trapped by the crystalline domain walls in
FeSe$_{0.45}$Te$_{0.55}$. Here, we perform the first-principles calculations to
show that iron atoms in the domain wall spontaneously form the ferromagnetic
order in line with orientation of the wall. The ferromagnetism can impose a
$\pi$ phase difference between the domain-wall-separated surface
superconducting regimes under the appropriate width and magnetization of the
wall. Accordingly, the topological surface superconducting state of
FeSe$_{0.45}$Te$_{0.55}$ can give rise to one-dimensional Majorana modes
trapped by the wall. More interestingly, we further propose a surface junction
in the form of FeSe$_{0.45}$Te$_{0.55}$/ferromagnet/FeSe$_{0.45}$Te$_{0.55}$,
which can be adopted to create and fuse the Majorana zero modes through
controlling the width or magnetization of the interior ferromagnetic barrier.
The braiding and readout of Majorana zero modes can be realized by the designed
device. Such surface junction has the potential application in the
superconducting topological quantum computation.
