Sklyanin-like algebras for (<i>q</i>-)linear grids and (<i>q</i>-)para-Krawtchouk polynomials

S-Heun operators on linear and $q$-linear grids are introduced. These special cases of Heun related to Sklyanin-like algebras. The Continuous Hahn Big $q$-Jacobi polynomials functions which these have natural actions. We show that the encompass both bispectral Kalnins Miller's structure operators. four realize limit trigonometric degeneration original Sklyanin algebra. Finite-dimensional representations algebras obtained from a truncation condition. corresponding representation bases finite families polynomials: para-Krawtchouk $q$-para-Krawtchouk ones. A algebraic interpretation had been missing is thus obtained. also recover attached problems as quadratic combinations