Supply voltage has no effect on the offset. Temperature, on the other hand, has a slight effect. This change is notified in the datasheet as "Average Input Offset Voltage Drift" in μV/oC.
The offset can be trimmed by setting up a PGA offset reference block in which the input is set to AGND and the reference to VSS and the output of the block is fed to the reference of the input PGA block. The gain of this offset reference block can be set to adjust out the overall offset of the input block.