The kasra on ḍād in الْقَاضِيَ is not the accusative ending; it precedes the final yāʾ as part of the noun’s form.
The accusative fatḥa is on the final يَ: الْقَاضِيَ.
Compare: رَأَيْتُ الْعَصَا has an estimated fatḥa, while رَأَيْتُ الْقَاضِيَ has a visible fatḥa. Both are accusative objects.