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Texas and the Biden administration exchanged lawsuits on Thursday regarding the federal government’s coronavirus vaccine mandate and voting rights. 

"Biden just announced his plan to wield OSHA to mandate vaccines on private businesses," Texas’ Republican Attorney General posted on Twitter Thursday. "And I’m announcing my plan to sue him once this illegal, unconstitutional regulation hits the Federal Register. Here comes another winning #Texas v. Biden law suit!"

Texas Gov. Greg Abbott, l, and Attorney General Ken Paxton hold a press conference to address a Texas federal court's decision on the immigration lawsuit filed by 26 states challenging President Obama. Paxton was indicted Monday on three counts of securities fraud unrelated to his official duties. (Photo by Robert Daemmrich Photography Inc/Corbis via Getty Images) (Getty Images)

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The Occupational Safety and Health Administration is giving employers with more than 100 employees a Jan. 4 deadline to comply with President Biden's COVID-19 vaccine mandate and threatening thousands of dollars in fines for defiant businesses, according to a fact sheet released by the White House Thursday.

Also on Thursday, Biden’s Justice Department announced that it is suing Texas over an election integrity bill signed into law in September aimed at combating voter fraud. 

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"The U.S. Justice Department announced today that it has filed a lawsuit against the State of Texas and the Texas Secretary of State over certain restrictive voting procedures imposed by Texas Senate Bill 1, which was signed into law in September 2021," the DOJ statement read. "The United States’ complaint challenges provisions of Senate Bill 1 under Section 208 of the Voting Rights Act and Section 101 of the Civil Rights Act of 1964."

Attorney General Merrick Garland testifies before a Senate Judiciary Committee hearing examining the Department of Justice on Capitol Hill in Washington, Wednesday, Oct. 27, 2021. (Tasos Katopodis/Pool via AP) (Tasos Katopodis/Pool via AP)

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Paxton responded to the lawsuit against Texas on Twitter pledging to the Biden administration that he will "see you in court."

Texas and the Biden administration are also currently involved in a legal spat over abortion and the U.S. Supreme Court heard oral arguments this week on Texas' controversial newly enacted law banning abortions after a fetal heartbeat can be detected.

Anti-abortion demonstrators pray and protest outside of a Whole Women's Health of North Texas, Friday, Oct. 1, 2021, in McKinney, Texas. A federal judge did not say when he would rule following a nearly three-hour hearing in Austin during which abortion providers sought to block the nation's most restrictive abortion law, which has banned most abortions in Texas since early September. (AP Photo/Brandon Wade) (AP Photo/Brandon Wade)

To date, Paxton has won or joined winning lawsuits against the Biden administration on border and energy policies. 

Paxton has sued the Biden administrations including in October when Texas filed a lawsuit to force the Biden administration to continue building a wall at the southern border that Congress had already appropriated money for.

In March, Texas sued Biden to reinstate a permit for the Keystone XL pipeline that was derailed by the Biden administration. Texas also sued Biden earlier this year over his administration's pause on oil and gas drilling.

Fox News’ Michael Lee contributed to this report