differential ADC full scale signal
This answer was made prior to the OP revealed that his inputs were AC coupled to the ADC hence, in the text below, it was presumed he was making a DC connection to the ADC: -
But my single ended signal never becomes negative; It swings from 0V to 0.5V. 
Then, in comments: -
I have an opamp that centers it to 0.95V and outputs the differential signals with a gain of 1.
Given that it now is revealed to be an AC connection, there are no constraints on the mid-voltage-range of the preceding stage being centred at 2.5 volts, providing that series resistors are used to feed the ADC inputs in order to limit input current to levels that should be prescribed by the ADC data sheet.

The ADS4249 has a VCM voltage of 0.95 volts: -

This means that for each input, the full scale signal needs to swing from +0.45 volts to +1.45 volts (a single-ended difference of 1 volt and an overall differential difference of 2 volts).

But my single ended signal never becomes negative. It swings from 0V
to 0.5V.

OK, you need to adjust this so that it is centred on +0.95 volts and not +2.5 volts. Then, you need to reduce the maximum swings to that required by the ADC.
Resistors will be your friends here but make sure you observe this: -