Hi Shashank,
Welcome to the TI E2E forums.
The ADS1259 can measure differential voltages as large as +/-Vref. However, the input voltage range is also limited by the ADS1259 supply rails. Are you ensuring that your precision supply is referenced to the same ground potential as the ADS1259?
Do you have a schematic or other information you can share?
Best Regards,
Chris