Following the Post's report, Trump sued James, arguing that she was violating his constitutional rights with a politically motivated investigation.
"Despite numerous attempts to delay our investigation by the Trump Organization, we are confident that our questions will be answered and the truth will be uncovered because no one is above the law," said a spokesperson for James on Monday.
The Trumps urged a court to "quash" the subpoenas, a legal filing showed.
"Her (James's) actions are a threat to our democracy and I plan to hold her accountable to the fullest extent," said Trump lawyer Alina Habba.
James is probing whether the Trump Organization may have illegally reported false values on its properties, potentially to gain banking and tax advantages.
She launched her investigation in March 2019 and suspects that the Trump Organization fraudulently overstated the value of certain properties when seeking bank loans, and later reported much smaller values when declaring assets so it could pay less tax.
Trump's son Eric, who is executive vice president of the Trump Organization, was interviewed by James's office on the issue in October 2020.
The former president is facing pressure from several legal probes.
In Washington he is trying to prevent a congressional probe into the January 6 attack by his supporters on the US Capitol from accessing White House records related to that day.
The Trump Organization is under investigation by the Manhattan district attorney for possible financial crimes and insurance fraud.
In July, the Trump Organization and its long-serving finance chief, Allen Weisselberg pleaded not guilty in a New York court to 15 felony fraud and tax evasion charges.
His trial is due to begin in the middle of this year.
Trump was also questioned for more than four hours in October as part of a lawsuit by a group of protestors who allege that his security guards assaulted them six years ago.
He is also battling to prevent years of his tax returns from being released to prosecutors.