Dark matter (DM) particles in our Galaxy can be gravitationally trapped by the Sun. Their annihilation and decay can lead to final states with Standard Model (SM) particles, including gamma rays. In a possible scenario, DM particles can be captured in external orbits. In this case, gamma rays produced in DM annihilations and decays can be detected on Earth. In another possible scenario, DM particles are accumulated in the Solar core. In this case, their annihilation/decay products will likely be absorbed in the Sun. However, in this framework, some theoretical scenarios suggest that DM particles can annihilate into long-lived mediators, which are able to escape from the Sun and decay into final state with gamma rays detectable on Earth. All these processes would result in an excess in the gamma-ray spectrum from the Sun. We have analyzed a set of gamma-ray data collected by the Fermi Large Area Telescope (LAT) during its first 13.5 years of operation to search for possible excesses in the Solar spectrum. Since no excess is found, we set constraints on the DM-nucleon scattering cross-sections.