We examine the fractional complex scalar field within a limited system and apply the Hamilton-Jacobi method to it. As a result, we obtain the simplified stage space Hamiltonian density excluding needing additional gauge fixing constraints or conformable fractional Lagrange multipliers. We also explore the quantization of this system. Alternatively, we can derive the path integral for these systems by integrating over the canonical phase space coordinates (φ,A), which eliminates the need for any gauge fixing constraints. On another note, our motivation to investigate the parameterization of conformable fractional time stems from the drawbacks of the conventional Hamiltonian approach in classical fields. Although the Lagrangian formulation maintains relativistic covariance, the unique role of time prevents the construction of a Hamiltonian formulation that treats x, y, z, and time symmetrically.