What your ex-girlfriend is doing is basically blackmailing.
Blackmail is the action of threatening to reveal a secret about someone, unless they do something you tell them to do, such as giving you money. It’s better to communicate with her about this matter. This is a huge matter and your reputation is at stake. To avoid any kind of mishap, you can file a complaint of blackmailing against her. Blackmailing can possibly fall under the categories of Criminal Intimidation or Extortion, both being punishable offenses under the Indian Penal Code 1860. Blackmailing can be Criminal Intimidation under Section 503 of the Indian Penal Code, 1860.