  Quantum materials with stacking van der Waals (vdW) layers that can host
non-trivial band structure topology and magnetism have shown many interesting
properties. Here using high-throughput density functional theory calculations,
we design and predict tetragonal vdW-layered quantum materials in the
MPd$_5$I$_2$ structure (M=Ga, In and 3d transition metals). Our study shows
that besides the known AlPd$_5$I$_2$, the -MPd$_5$- structural motif of
three-layer slabs separated by two I layers can host a variety of metal
elements giving arise to topological interesting features and highly tunable
magnetic properties in both bulk and single layer 2D structures. Among them,
TiPd$_5$I$_2$ and InPd$_5$I$_2$ host a pair of Dirac points and a likely strong
topological insulator state for the band manifolds just above and below the top
valence band, respectively, with their single layers possibly hosting quantum
spin Hall states. CrPd$_5$I$_2$ is a ferromagnet with a large out-of-plane
magneto-anisotropy energy, desirable for rare-earth-free permanent magnets.
