  We undertake the construction of quadratic parity-violating terms involving
the curvature in the four-dimensional metric-affine gravity. We demonstrate
that there are only 12 linearly independent scalars, plus an additional one
that can be removed by using the Pontryagin invariant. Several convenient bases
for this sector are provided in both components and differential form notation.
We also particularize our general findings to some constrained geometries like
Weyl-Cartan and metric-compatible connections.
