  We construct a new class of three-dimensional topological quantum field
theories (3d TQFTs) by considering generalized Argyres-Douglas theories on $S^1
\times M_3$ with a non-trivial holonomy of a discrete global symmetry along the
$S^1$. For the minimal choice of the holonomy, the resulting 3d TQFTs are
non-unitary and semisimple, thus distinguishing themselves from theories of
Chern-Simons and Rozansky-Witten types respectively. Changing the holonomy
performs a Galois transformation on the TQFT, which can sometimes give rise to
more familiar unitary theories such as the $(G_2)_1$ and $(F_4)_1$ Chern-Simons
theories. Our construction is based on an intriguing relation between
topologically twisted partition functions, wild Hitchin characters, and chiral
algebras which, when combined together, relate Coulomb branch and Higgs branch
data of the same 4d $\mathcal{N}=2$ theory. We test our proposal by applying
localization techniques to the conjectural $\mathcal{N}=1$ UV Lagrangian
descriptions of the $(A_1,A_2)$, $(A_1,A_3)$ and $(A_1,D_3)$ theories.
