  In twisted bilayer semiconductors with arbitrary twisting angles, a chiral
excitonic system can arise from the interlayer electron-hole Coulomb exchange
interaction (F\"{o}rster coupling) that hybridizes the anisotropic intralayer
excitons from individual layers. We present a general framework for the
effective exciton Hamiltonian taking into account the electron-hole Coulomb
exchange, using twisted homobilayer systems composed of transition metal
dichalcogenides or black phosphorus as examples. We demonstrate that such
chiral excitonic systems can feature unconventional Hall (Nernst) effects
arising from quantum geometric properties characteristic of the layer
hybridized wavefunctions under the chiral symmetry, for example, the
time-reversal even layer Hall counter flow and the crossed nonlinear dynamical
Hall effect, when mechanical and statistical force (temperature or density
gradient) drives the exciton flow.
