The correct option is A I > III > II
For the given molecules, the basicity depends on the extent to which the electron density is available at the nitrogen of the −NH2 group at the ipso position. Chlorine group is deactivating in nature as it tends to reduce the density of electrons via inductive effect. Although each chlorine atom does have several lone pairs, there is hardly any conjugation into the benzene ring. The lack of conjugation is due to the difference in energies between the orbitals of carbon and chlorine (they belong to different periods).
The nitro group is even stronger in terms of its ability to withdraw electrons away from the benzene ring. But the manner in which the nitro group withdraws electrons – conjugation versus inductive effect - will depend on where it is positioned with respect to the ipso −NH2 group. At the ortho and para positions, the electron withdrawing effect of the −NO2 group is more pronounced because of conjugation. The same group, when it is present at the meta position, is electron withdrawing to a lesser extent via the inductive effect (alone!). Clearly, the dichloroaniline will be the most basic as the ipso −NH2 will have the greatest availability of electron density at the nitrogen atom. On the other hand, the molecule 4-chloro-2-nitroaniline will be the least basic.
Hence, I > III> II