Topology and correlation, fundamental ingredients that often dictate the ground states of quantum matter, leave distinct local electronic fingerprints that can be detected with scanning tunneling microscopy (STM). In this dissertation, we first introduce a unique spin signature of Majorana zero mode (MZM) in atomic chains and present how we detect it using spin-resolved measurements with a STM. Second, we will describe a series of experiments demonstrating how the combined influence of magnetism and superconductivity on the one-dimensional helical hinge channel of a higher-order topological insulator can give rise to a MZM. Last, we will discuss unusual spectroscopic characteristics found on magic angle twisted bilayer graphene (MATBG) over a wide range of carrier densities, including where superconductivity has been reported to emerge, and how these correlated features allow us to estab- lish a more concrete connection between MATBG and high-Tc cuprates beyond the phenomenological resemblance of their transport phase diagrams.