Which of the conditions are essential for enhanced punishment to an offender with previous conviction ?

Under Section 13 of the Bharatiya Nyaya Sanhita, 2023 (formerly section 75 IPC), enhanced punishment on a previous conviction applies only where the earlier and the later offence both fall under Chapter X (coin, currency-notes, bank-notes and Government stamps) or Chapter XVII (offences against property), so the essential condition is that "The offence must be an offence relating to property or coin or government stamp". Both offences must be punishable with imprisonment of three years or upwards, but the sentence actually passed on the earlier conviction is irrelevant, and the earlier conviction must be by a Court in India.