The main purpose of this study is to construct a new type special number system which is defined as generalized Padovan Pauli quaternion with non-negative and negative subscripts. Furthermore, we give some special cases with respect to the initial values and examine them, as well. We obtain not only new equations but also recurrence relations, Binet formulas, generating functions, exponential generating functions, summation formulas, and special determinant equalities with a numerical example regarding this new number system. After all, we construct algorithms for calculating the generalized Padovan Pauli quaternions with non-negative and negative subscripts. Then, we present the \(\mathbb {R}\) -linear transformation of this new type special Pauli quaternions.