The correct order of ionic radii is:

For isoelectronic species (species with the same number of electrons), the ionic radius decreases as the atomic number (nuclear charge) increases.${\text{N}}^{3-},{\text{Mg}}^{2+},{\text{Al}}^{3+}$ all have $10$ electrons.Atomic numbers: $N=7,Mg=12,Al=13$.Since $N$ has the smallest nuclear charge, its radius is the largest. Since $Al$ has the largest nuclear charge, its radius is the smallest.Order: ${\text{N}}^{3-}>{\text{Mg}}^{2+}>{\text{Al}}^{3+}$.