  We reformulate the Chern-Simons modified gravity in the metric-affine
formalism, by enlarging the Pontryagin density with homothetic curvature terms
which restore projective invariance without spoiling topologicity. The latter
is then violated by promoting the coupling of the Chern-Simons term to a
(pseudo)-scalar field. We derive the perturbative solutions for torsion and
nonmetricity from the background fields, and we describe the dynamics for the
resulting linearized metric and the scalar fields in a Schwarzschild black hole
background. Then, by adopting numerical techniques we compute the quasinormal
mode spectrum and the late-time tails for scalar and metric perturbations.
