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Florida Congressman Cory Mills allegedly threatened to leak a pageant queen's sex tapes after she dumped him ... according to a shocking new report.

The Republican representative from the Sunshine State's 7th District has been accused by Lindsey Langston -- a Florida Republican state committee member and winner of the 2024 Miss United States beauty pageant. United States National Pageants

Cops say Langston told them Mills contacted her numerous times and threatened to release nude images and videos of them having sex after they split ... and, cops also put in the report that she showed them texts of the alleged threats.

Langston filed the report on Mills on July 14 for those alleged threats ... and, cops say she also accused him of threateni

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