Getting blackmailed by a escort service

What you are on the receiving end of is - blackmailing and yes, blackmailing is a criminal offence in India.
It is considered a form of extortion and is punishable under Sections 383 and 389 of the Indian Penal Code, 1860 (IPC).

Section 383 of the IPC defines extortion as the act of intentionally putting a person in fear of injury to their person, reputation, or property, with the intention of illegally obtaining property or any valuable security. The punishment for extortion is imprisonment for up to three years or a fine, or both.

Section 389 of the IPC defines the offence of putting a person in fear of accusation of an offence in order to commit extortion. The punishment for this offence is imprisonment for up to ten years, along with a fine.

So, if someone is blackmailing you in India, you can report it to the police and get an FIR lodged with the nearest police station. The police will investigate the matter and take appropriate action against the accused.
?Alternatively, you can get a complaint filed with the nearest Area Magistrate under Section 383 or 389 of the IPC.

Additionally, it is important not to give in to the demands of the extortionist. Giving in will only encourage them to continue their illegal activities. Collect any evidence that you can, such as text messages, emails, or voicemails. Keep a record of all interactions with the extortionist. Also, take precautions to protect yourself, such as changing your phone number, blocking the extortionist's number, or seeking protection from the police.