The party seeks reversal of the judgment which disqualified its candidate David Lyon in the last governorship election.
Babalola is urging the court to set aside the judgment.
He noted that the court has jurisdiction and powers to set aside its own judgment, if the judgment is obtained by fraud, if the court was misled or the judgment was given outside jurisdiction, which is one of the grounds of their application.
He also argued that the judgment delivered on 13 February breached the applicant rights to fair hearing.
The party argued that the Supreme Court acted without jurisdiction and denied it fair hearing when it proceeded to disqualify its governorship candidate even though the Federal High Court, in the judgment by Justice Inyang Ekwo, which the apex court affirmed, refused the prayer to disqualify Mr Lyon.
Attending the proceedings are the National Chairman of the All Progressives Congress, Adams Oshiomole and the disqualified deputy Governor elect of the APC, Senator Degi Biobarakuma. Also in court is the governor of Bayelsa State, Duoye Diri.
The 7 member panel of the Justices of the Supreme court is led by Justice Sylvester Ngwuta.
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