We study the joint effect of disorder and Coulomb interaction screening on the exciton spectra in two-dimensional (2D) structures. These can be van der Waals structures or heterostructures of organic (polymeric) semiconductors as well as inorganic substances like transition metal dichalcogenides. We consider 2D screened hydrogenic problem with Rytova - Keldysh interaction by means if so-called fractional Scrodinger equation. Our main finding is that above synergy between screening and disorder either destroys the exciton (strong...