ATLANTA—Former President Donald Trump asked a court to scrap the criminal investigation in Georgia into his and his allies’ efforts to overturn the state’s presidential election, saying Fulton County District Attorney Fani Willis ’s office should be disqualified from the probe and the work of a special grand jury should be thrown out. Mr. Trump’s motion, filed on Monday with a state court in Atlanta, came days after he said he expected criminal charges in a separate New York investigation connected to the payment of hush money to a porn star.

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