The correct chronological order of the Magadhan dynasties is IV, II, I, and III.

Option 1 is incorrect because it places the Mauiyas dynasty (III) before the Sisunagas dynasty (II), which is incorrect.

Option 2 is incorrect because it places the Nandas dynasty (I) before the Sisunagas dynasty (II), which is incorrect.

Option 3 is correct as it correctly places the Haiyankas dynasty (IV) before the Sisunagas dynasty (II), followed by the Nandas dynasty (I), and then the Mauiyas dynasty (III).

Option 4 is incorrect as it places the Mauiyas dynasty (III) after the Nandas dynasty (I), which is incorrect.

Overall, option 3 is the correct answer.