Externally applied electric field and effective radius effects are investigated on the lowest excitedstate shallow-donor binding energy in (In,Ga)N-GaN parabolic wire within the framework of single band effective-mass approximation. The calculations are performed using the finite-difference method within the quasi-one-dimensional effective potential model. Our results reveal that: (i) the probability density is the largest on a circularity whose radius is the effective radius, (ii) the lowest excited-state binding energy is the largest for impurity located on this circularity while it starts to decrease when the impurity is away from the circularity and (iii) the binding energy is strongly-dependent on the complex interplay of spatial confinement, coulomb interaction and applied electric field.