  Andreev bound states trapped in a multi-terminal Josephson junction (JJ) can
be assigned a synthetic band topology owing to their periodic dependence on the
Josephson phase bias. We demonstrate that the BdG symmetry adds a twist to this
topological character, i.e., gap closing points may or \textit{may not}
correspond to change of Chern number, hence extending the standard paradigm for
topological bands. We further show that the topology of Andreev bands depends
only on the scattering matrix of the junction and is independent of the
topological nature of superconductors forming the JJ hence indicating a
universal behaviour of multi-terminal JJ. We also show that the chiral
junction, supported by quantum Hall state at the junction region, leads to flat
Andreev bands (implying absence of DC Josephson effects) that are devoid of
Berry curvature ( implying absence of AC Josephson effects). Such electrically
inert JJ may be useful for storage of quantum information in future quantum
devices.
