This study aims to develop a new algebra based on the Minkowskian product or relativistic Lorentz invariants. This leads to the notion of q- invariant algebras, defining q- deformed quadratic relativistic algebras and establishing some q- differential operators and derivations. Then, from these algebras, we define the q- relativistic invariant function on a free algebra k⟨x, y, z, u⟩ with the objective of formulating the q- differential quadratic operators. On the other hand, we define the q- quadratic differential operators on the Clifford algebra Cl0,n. We consider the case of a polynomial function in the noncommutative quadratic variables x2, y2, z2 and u2, obtaining the q- differential quadratic operators for these functions with their respective properties. Furthermore, we formulate the q- quadratic Dirac differential operators. On the other hand, on the algebra Ψ with the generators x, y, we have proposed the extended derivation with its corresponding properties, in order to apply it to the q- relativistic invariant algebras and make a relationship with the q- Dirac quadratic operators. On a function of non-commutative quadratic variables, we define the q- quadratic differentiation operators Dq2 with their properties, and finally some applications for further work.