This paper explores a family of "classical" orthogonal polynomials that satisfy an eigenvalue problem with a Dunkl-type differential operator, derived from the little $q$-Jacobi polynomials in the limit $q = -1$. These polynomials are shown to provide a nontrivial realization of the Askey-Wilson algebra for $q = -1$. The authors construct the general solution of the eigenvalue equation and derive explicit expressions for the corresponding little -1 Jacobi polynomials. They also demonstrate that these polynomials are Dunkl-classical, meaning they satisfy an eigenvalue equation involving a combination of a differential operator and a reflection operator. The paper further discusses the relationship between these polynomials and symmetric Jacobi polynomials, and explores their Dunkl-classical properties. Additionally, it examines the Askey-Wilson algebra relations for the little -1 Jacobi polynomials and provides a special case where the polynomials satisfy a "square root" of the Schrödinger operator, with a quantum mechanical interpretation.This paper explores a family of "classical" orthogonal polynomials that satisfy an eigenvalue problem with a Dunkl-type differential operator, derived from the little $q$-Jacobi polynomials in the limit $q = -1$. These polynomials are shown to provide a nontrivial realization of the Askey-Wilson algebra for $q = -1$. The authors construct the general solution of the eigenvalue equation and derive explicit expressions for the corresponding little -1 Jacobi polynomials. They also demonstrate that these polynomials are Dunkl-classical, meaning they satisfy an eigenvalue equation involving a combination of a differential operator and a reflection operator. The paper further discusses the relationship between these polynomials and symmetric Jacobi polynomials, and explores their Dunkl-classical properties. Additionally, it examines the Askey-Wilson algebra relations for the little -1 Jacobi polynomials and provides a special case where the polynomials satisfy a "square root" of the Schrödinger operator, with a quantum mechanical interpretation.