The key motivation for my research during Ph.D. lies in the intriguing possibility of extracting crucial information about Andreev bound states (ABS) from mesoscopic transport phenomena. These kinds of mesoscopic transport can be explored by applying either a voltage or temperature bias. However, applying a voltage bias across a Josephson junction (JJ) transforms it into a time-dependent problem, introducing additional complexities. On the other hand, thermal bias-induced transport offers a viable platform for exploring fundamental physics without the above-mentioned issues. Once a temperature bias is applied, one can measure either heat or charge currents across a JJ. We have focused on identifying signatures of ABS through these thermal bias-induced currents. Using the well-known Bogoliubov-de Gennes (BdG) Hamiltonian, we aim to model superconducting heterojunctions, specifically JJs, in order to evaluate different transport coefficients such as thermoelectric/thermal current coefficient, thermal conductivity, differential conductance, and so on within the linear response limit. Furthermore, my research delves into the topological aspects of multiterminal JJs, including the topological nature of the superconductors, as well as the interplay between gap closure and the band topology of the Andreev bands.