Magic-angle twisted bilayer graphene (MATBG) harbors various exotic physical phenomena such as strongly correlated topological states, superconductivity, ferromagnetism etc. The flexibility of tuning the twist angle between the layers enhances the electron-electron interaction in the nearly flat band in these systems. Also, the tunability of carrier density by the electrostatic-gating in van der Waals heterostructures opens plethora of opportunities to study the rich phase diagram in such systems. In order to study strongly correlated states in two-dimensional van der Waals heterostructures, high quality materials are necessary requisite. The focus of this thesis will be to optimize sample quality, followed by conductance and noise measurements to investigate fractional Chern insulating (FCI) states in MATBG, and also understand the underlying mechanism of superconductivity in MATBG. To be more specific, a ballistic multi-terminal junction will be designed for detecting mechanism of superconductivity in MATBG. Local and non-local differential conductance serves as a good measure of the studying cooper-pair splitter, which refers to crossed-Andreev reflection, necessarily revealing, whether the superconductivity in MATBG is unconventional in nature. As cooper-pair splitting can provide insight in the entangled many-body state. On top of that, we also plan to detect Fano factor for shot noise to study superconductivity in MATBG. Study of correlated insulating states in similar system will also be carried out, with a final goal to observe FCIs in absence of external magnetic field. The overall goal of this thesis will be to study the twisted multi-layer (bi, tri, qudra etc.) graphene systems via conductance and noise measurements to understand the rich phase diagram of the strongly correlated electrons in such systems.