New Jersey gubernatorial candidate Mikie Sherrill is facing fresh scrutiny following the revelation that her two children were accepted into the highly competitive Naval Academy — days after her campaign was rocked by news of her involvement in a notorious cheating scandal as a cadet.

The Democratic congresswoman’s office announced in June that her two kids, Lincoln and Margaret Hedberg, were among nine students from her district to land spots in the Naval Academy, which has a slim admission rate of 9%.

Sen. Cory Booker (D-NJ) and former interim Sen. George Helmy (D-NJ) each nominated one of the two children, The Post has learned. Members of Congress can “can have five constituents attending the Naval Academy at any time” and typically nominate 15 candidates for each vacant spot with

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