What are the people who study ancient coins called?

Numismatists

The correct answer is Option 1 - Numismatists

People who study ancient coins are called Numismatists.

Punch-marked coins made of silver and copper (c. sixth century BCE onwards) were amongst the earliest to be minted and used. These have been recovered from excavations at a number of sites throughout the subcontinent. Numismatists have studied these and other coins to reconstruct possible commercial networks. Attempts made to identify the symbols on punchmarked coins with specific ruling dynasties, including the Mauryas, suggest that these were issued by kings. It is also likely that merchants, bankers and townspeople issued some of these coins. The first coins to bear the names and images of rulers were issued by the Indo-Greeks, who established control over the north-western part of the subcontinent c. second century BCE. The kushanas, however, issued the largest hoards of gold coins first gold coins c. first century CE.