The correct answer is option 1, Ramprasad Bismil. The Kakori Dacoity case refers to a train robbery that took place in Kakori, Uttar Pradesh, during the Indian independence movement in 1925. Ramprasad Bismil was one of the key leaders of the Hindustan Republican Association (HRA), which was involved in the robbery. The aim of the robbery was to obtain funds for the revolutionary activities against British rule.

Bhagat Singh, mentioned in option 2, was a prominent freedom fighter but was not directly involved in the Kakori Dacoity case.

Batukeshwar Datta, mentioned in option 3, was a member of the HRA and was present during the Kakori Dacoity, but he cannot be considered the hero of the case.

Barkatulla, mentioned in option 4, does not have any significant connection to the Kakori Dacoity case.

Therefore, option 1, Ramprasad Bismil, is the correct answer as he played a crucial role in planning and executing the Kakori Dacoity.