  Hitchin in [Duke Math. J. 54 (1), 91-114 (1987)] introduced a proper morphism
from the moduli space of stable $G$-Higgs bundles
($G=\mathrm{GL}(n,\mathbb{C}),\mathrm{Sp}(2m,\mathbb{C})$ and
$\mathrm{SO}(n,\mathbb{C})$) over a curve to a vector space of invariant
polynomials and he described the generic fibers of that morphism. In this
paper, we first describe the generic Hitchin fibers for the moduli space of
stable parabolic projective symplectic/orthogonal Higgs bundles without fixing
the determinant. We also describe the generic fibers when the determinant is
trivial.
