Stacking-dependent anisotropic altermagnetism in V$_{1/3}$NbS$_2$

We report profound impacts of the stacking sequence of triangular lattices of magnetic transition metal ions intercalated between the layers of the van der Waals material NbS$_2$. Using single crystal x-ray and neutron diffraction, and transport and magnetization measurements, we show there are two distinct polytypes of $\rm V_{1/3}NbS_2$ with disparate easy axes of magnetization and different anomalous Hall responses. Self-consistent analysis of inelastic neutron scattering data provides evidence for oscillatory RKKY interactions that extend to 1 nm and stabilize quasi-collinear A-type altermagnetic orders in both polytypes though with perpendicular easy axes. The detailed stacking sequence of a bulk polytype crystal dramatically impact its macroscopic anomalous Hall response and magnetism, which suggests a new path to engineer the bulk properties of a layered three dimensional solid.