  We study the quantization of two versions of unimodular gravity, namely,
fully diffeomorphism-invariant unimodular gravity and unimodular gravity with
fixed metric determinant utilizing standard path integral approach. We derive
the BRST symmetry of effective actions corresponding to several relevant gauge
conditions. We observe that for some gauge conditions, the restricted gauge
structure may complicate the formulation and effective actions, in particular,
if the chosen gauge conditions involve the canonical momentum conjugate to the
induced metric on the spatial hypersurface. The BRST symmetry is extended
further to the finite field-dependent BRST transformation, in order to
establish the mapping between different gauge conditions in each of the two
versions of unimodular gravity.
