  A spin-$\frac{1}{2}$ subsystem conjoined along a cut with a subsystem of
spinless fermions in the state of topological insulator is studied on a
honeycomb lattice. The model describes a junction between a 2D topological
insulator and a 2D spin lattice with direction-dependent exchange interactions
in topologically trivial and nontrivial phase states. The model Hamiltonian of
the complex system is solved exactly by reduction to free Majorana fermions in
a static $\mathbb{Z}_2$ gauge field. In contrast to junctions between
topologically trivial phases, the junction is defined by chiral edge states and
direct interaction between them for topologically nontrivial phases. As a
result of the boundary interaction between chiral edge modes, the edge junction
is defined by the Chern numbers of the subsystems: such the gapless edge modes
with the same (different) chirality switch on (off) the edge current between
topological subsystems. The sign of the Chern number of spin subsystem is
changed in an external magnetic field, thus the electric current strongly
depends both on a direction and a value of an applied weak magnetic field. We
have provided a detailed analysis of the edge current and demonstrate how to
switch on (off) the electric current in the magnetic field.
