The correct answer is option 3 - Ibn Battuta. Ibn Battuta is a famous Moroccan explorer who traveled extensively during the 14th century. He is known for his detailed accounts of his travels, which provide valuable information about the societies and cultures he encountered. In his writings, Ibn Battuta described the medieval Indian postal system as having two types of messengers - the horse-post called `Ulu` and the foot-post called `Dawa`. These messengers were responsible for delivering important messages and letters across different regions in India during that time.

Al-Biruni, option 1, was a renowned Persian scholar who made significant contributions to various fields such as astronomy, mathematics, and geography. However, there is no evidence to suggest that he described the medieval Indian postal system.

Daurte Barbose, option 2, is not a known historical figure, and there is no information available about their connection to the medieval Indian postal system.

Seydi Ali Reis, option 4, was an Ottoman admiral and mapmaker who recorded his experiences in the Mediterranean Sea. There is no mention of him describing the Indian postal system in his accounts.

Therefore, the correct answer is option 3 - Ibn Battuta.