No, the WebSocket Quote mode does not include exchange timestamp details. It provides fields such as OHLC, Last Traded Price (LTP), Last Traded Quantity (LTQ), Volume, and Market Depth. If you require last_trade_time and exchange_timestamp, you must subscribe to the instrument in Full mode, as these fields are available only in the Full tick packets. The same is explained correctly in the packet structure documentation. You may refer to the similar discussion here.
Quote modedoes not include exchange timestamp details. It provides fields such as OHLC, Last Traded Price (LTP), Last Traded Quantity (LTQ), Volume, and Market Depth. If you require last_trade_time and exchange_timestamp, you must subscribe to the instrument in Full mode, as these fields are available only in the Full tick packets. The same is explained correctly in the packet structure documentation. You may refer to the similar discussion here.