There is no Scepter of Darkness in Shadow the Hedgehog. You are
probably referring to Sonic the Hedgehog Next Gen/2006. Rouge has
the Scepter of Darkness at the beginning of the game; you get the
Scepter of Darkness after saving Rouge after the first level in
Shadow's Story, White Acropolis. Later in the story (but in the
past in chronological time), the dying Duke of Soleanna gives
Shadow the Scepter in order to seal Mephiles.