Step 1: Understanding the Concept:
State-wise leading livestock production and populations are documented under the official Livestock Census reports.
Step 2: Detailed Explanation:
Matching species in List I with leading states in List II:
1. Poultry (A) $\to$ Tamil Nadu (II) (Tamil Nadu leads in total poultry and commercial layer population).
2. Cattle (B) $\to$ West Bengal (IV) (West Bengal has the highest cattle population in the 20th Livestock Census).
3. Fish (C) $\to$ Andhra Pradesh (I) (Andhra Pradesh is the premier state in total fish and inland aquaculture production).
4. Sheep (D) $\to$ Telangana (III) (Telangana leads the country in sheep population).
Step 3: Final Answer:
Matching summary: A $\to$ II, B $\to$ IV, C $\to$ I, D $\to$ III.