  We initiate the study of boundary Vertex Operator Algebras (VOAs) of
topologically twisted 3d $\mathcal{N}=4$ rank-0 SCFTs. This is a recently
introduced class of $\mathcal{N}=4$ SCFTs that by definition have
zero-dimensional Higgs and Coulomb branches. We briefly explain why it is
reasonable to obtain rational VOAs at the boundary of their topological twists.
When a rank-0 SCFT is realized as the IR fixed point of a $\mathcal{N}=2$
Lagrangian theory, we propose a technique for the explicit construction of its
topological twists and boundary VOAs based on deformations of the
holomorphic-topological twist of the $\mathcal{N}=2$ microscopic description.
We apply this technique to the $B$ twist of a newly discovered family of 3d
$\mathcal{N}=4$ rank-0 SCFTs ${\mathcal T}_r$ and argue that they admit the
simple affine VOAs $L_r(\mathfrak{osp}(1|2))$ at their boundary. In the
simplest case, this leads to a novel level-rank duality between
$L_1(\mathfrak{osp}(1|2))$ and the minimal model $M(2,5)$. As an aside, we
present a TQFT obtained by twisting a 3d $\mathcal{N}=2$ QFT that admits the
$M(3,4)$ minimal model as a boundary VOA and briefly comment on the classical
freeness of VOAs at the boundary of 3d TQFTs.
