Using the effective mass approximation and the finite difference method, we examined the linear, non-linear, and total optical absorption coefficients (OAC), as well as the relative refractive index coefficients (RIC) variations for an off-center shallow donor impurity in a 2D-curved electronic nanostructure subjected to external electric and magnetic fields. Our results reveal that the peak positions of the OAC and RIC are susceptible to the geometrical angles, the impurity position, and the strength of the applied electric and magnetic fields. In particular, the positions of the OAC and RIC peaks can be shifted towards blue or red by adjusting the geometric angle. In addition, the amplitudes of these peaks are influenced by the application of external fields and by the position of the impurity. This knowledge is essential for understanding and optimizing the optical characteristics of 2D-Curved nanostructure for advanced optoelectronic applications.