  Quantum materials whose atoms are arranged on a lattice of corner-sharing
triangles, $\textit{i.e.}$, the kagome lattice, have recently emerged as a
captivating platform for investigating exotic correlated and topological
electronic phenomena. Here, we combine ultra-low temperature angle-resolved
photoemission spectroscopy (ARPES) with scanning tunneling microscopy and
density functional theory calculations to reveal the fascinating electronic
structure of the bilayer-distorted kagome material
$\textit{Ln}$Ti${_3}$Bi${_4}$, where $\textit{Ln}$ stands for Nd and Yb.
Distinct from other kagome materials, $\textit{Ln}$Ti${_3}$Bi${_4}$ exhibits
two-fold, rather than six-fold, symmetries, stemming from the distorted kagome
lattice, which leads to a unique electronic structure. Combining experiment and
theory we map out the electronic structure and discover double flat bands as
well as multiple van Hove singularities (VHSs), with one VHS exhibiting
higher-order characteristics near the Fermi level. Notably, in the magnetic
version NdTi${_3}$Bi${_4}$, the ultra-low base temperature ARPES measurements
unveil an unconventional band splitting in the band dispersions which is
induced by the ferromagnetic ordering. These findings reveal the potential of
bilayer-distorted kagome metals $\textit{Ln}$Ti${_3}$Bi${_4}$ as a promising
platform for exploring novel emergent phases of matter at the intersection of
strong correlation and magnetism.
