Hi Anil,
Thank you for the explanation.
Unfortunately there is no setting to make the ADC treat an input signal of 0V as +/-0.625V. The only way I can think of is to use a fully differential amplifier with the -ve input tied to 1.25V and the +ve input connected to your signal source to do the single ended to differential conversion. Take a look at this part: THS4120
Thanks,
Eben.