  We study the emergent band topology of subgap Andreev bound states in the
three-terminal Josephson junctions. We scrutinize the symmetry constraints of
the scattering matrix in the normal region connecting superconducting leads
that enable the topological nodal points in the spectrum of Andreev states.
When the scattering matrix possesses time-reversal symmetry, the gap closing
occurs at special stationary points that are topologically trivial as they
carry vanishing Berry fluxes. In contrast, for the time-reversal broken case we
find topological monopoles of the Berry curvature and corresponding phase
transition between states with different Chern numbers. The latter is
controlled by the structure of the scattering matrix that can be tuned by a
magnetic flux piercing through the junction area in a three-terminal geometry.
The topological regime of the system can be identified by nonlocal conductance
quantization that we compute explicitly for a particular parametrization of the
scattering matrix in the case where each reservoir is connected by a single
channel.
