  Topology plays a crucial role in many physical systems, leading to
interesting states at the surface. The paradigmatic example is the Chern number
defined in the Brillouin zone that leads to the robust gapless edge states.
Here we introduce the reduced Chern number, defined in subregions of the
Brillouin zone (BZ), and construct a family of Chern dartboard insulators
(CDIs) with quantized reduced Chern numbers in the sub-BZ (sBZ) but with
trivial bulk topology. CDIs are protected by mirror symmetries and exhibit
distinct pseudospin textures, including (anti)skyrmions, inside the sBZ. These
CDIs host exotic gapless edge states, such as M\"{o}bius fermions and midgap
corner states, and can be realized in photonic crystals. Our work opens up new
possibilities for exploring sBZ topology and nontrivial surface responses in
topological systems.
