Explanation:

- In January 2019, the National Museum of Indian Cinema in Mumbai was inaugurated by Prime Minister Narendra Modi.

- Option 1: Narendra Modi - The Prime Minister of India at the time, who inaugurated the museum.

- Option 2: Amitabh Bachchan - A renowned Indian film actor; he did not inaugurate the museum but is often involved in film-related events.

- Option 3: Ram Nath Kovind - The President of India at that time; however, he was not involved in the inauguration.

- Option 4: Devendra Fadnavis - The Chief Minister of Maharashtra then, who was likely present due to the location in Mumbai but did not inaugurate the museum.

Option 1: Narendra Modi is correct.