  A nonuniform in-plane Zeeman field can induce spontaneous supercurrents of
spin-orbit coupled electrons in superconducting two-dimensional systems and
thin films. In this work it is shown that current vortices can be created at
the ends of a long homogeneously magnetized strip of a ferromagnetic insulator,
which is deposited on the surface of a three-dimensional topological insulator.
The s-wave superconductivity on its surface is assumed to have an intrinsic
origin, or to be induced by the proximity effect. It is shown that vortices
with the odd vorticity can localize Majorana zero modes.The latter may also be
induced by sufficiently narrow domain walls inside the strip, that opens a way
for manipulating these modes by moving the walls. It is shown that the
vorticity can be tuned by varying the magnetization and width of the strip. A
stability of the strip magnetization with respect to the
Berezinsky-Kosterlitz-Thouless transition has been analyzed.
