This paper presents a family of "classical" orthogonal polynomials that satisfy a three-term recurrence relation and an eigenvalue problem involving a Dunkl-type differential operator. These polynomials are derived from the little q-Jacobi polynomials in the limit q = -1. They are shown to provide a nontrivial realization of the Askey-Wilson algebra for q = -1. The polynomials, referred to as little -1 Jacobi polynomials, are Dunkl-classical, meaning they satisfy an eigenvalue equation involving a combination of a differential operator and a reflection operator. The paper also explores the connection between these polynomials and symmetric Jacobi polynomials, and demonstrates that they can be obtained through Christoffel or Geronimus transformations. The study further shows that these polynomials satisfy the Askey-Wilson algebra relations and that they can be used to construct a "square root" of the Schrödinger operator in quantum mechanics. The paper concludes with a discussion of the physical significance of these results and their implications for the theory of orthogonal polynomials and quantum mechanics.This paper presents a family of "classical" orthogonal polynomials that satisfy a three-term recurrence relation and an eigenvalue problem involving a Dunkl-type differential operator. These polynomials are derived from the little q-Jacobi polynomials in the limit q = -1. They are shown to provide a nontrivial realization of the Askey-Wilson algebra for q = -1. The polynomials, referred to as little -1 Jacobi polynomials, are Dunkl-classical, meaning they satisfy an eigenvalue equation involving a combination of a differential operator and a reflection operator. The paper also explores the connection between these polynomials and symmetric Jacobi polynomials, and demonstrates that they can be obtained through Christoffel or Geronimus transformations. The study further shows that these polynomials satisfy the Askey-Wilson algebra relations and that they can be used to construct a "square root" of the Schrödinger operator in quantum mechanics. The paper concludes with a discussion of the physical significance of these results and their implications for the theory of orthogonal polynomials and quantum mechanics.