Uniqueness of $$\varvec{L}$$ function with special class of meromorphic function under restricted sharing of sets

The purpose of the paper is to rectify a series of errors occurred in (Banerjee and Kundu in Lithuanian Math J 41: 379–392, 2020, Sahoo and Sarkar in Ann Alexandru Ioan Cuza Univ Math 66:81–92, 2020, Yuan et al. in Lithuanian Math J 58:249–262, 2018) for a particular situation. To get a fruitful solution and to overcome the issue, we introduce a new form of set sharing namely restricted set sharing, which is stronger than the usual one. We manipulate the newly introduced notion in this specific section of literature to resolve all the complications. Not only that we have subtly used the same sharing form to a well known unique range set (Frank and Reinders in Complex Var Theory Appl 37:185–193, 1998) to settle a long time unsolved problem.