The fix is in with these city public school educators.

Teachers and their supervisors have used egregious — and often bizarre — tactics to tamper with tests in order to inflate student grades, according to records obtained by The Post.

Case in point: Department of Education probers substantiated allegations that Jane Winfield, a history teacher at Reynolds West Side High School on the Upper West Side, removed global-history Regents exams from an assistant principal’s office on Jan. 26, 2013.

She then improperly graded a section of the exams for 45 of her own students and inflated many of the scores, the DOE’s Office of Special Investigations found.

State rules bar teachers from grading their own students’ exams, the July 3, 2014, report by OSI investigator Robert Small notes.

Assistant Principal Mark Chenault told the OSI that he confronted Winfield about how she had gotten the exams. Winfield said that she removed them from Chenault’s office closet before he arrived at school and that she brought them to the library, where the tests were being graded.

Essay questions and short-answer questions require different scorers. Winfield was on the grading team for the global-history test at Reynolds HS, an alternative school for struggling students.

But she took exception to letting one scorer, a male teacher, also grade her exams. The tests were passed to another teacher.

“This behavior raised suspicion that she was doing something improper,” the OSI report said.

Another teacher grading the exams reported that he “observed Ms. Winfield inflate grades while transferring scores from students’ answer sheets to the official bubble sheet that was to be scanned into the computer,” the report said.

Afterward, then-Principal Jean McTavish and then-Assistant Principal Lilit Suffet, who is now the principal, examined the answer sheets of students whose exams Winfield graded. Their analysis found Winfield had graded at least one section of the exam for 45 of her students.

They forwarded the 45 exams she graded to the DOE’s Office of Assessment for analysis.

Officials there confirmed grade inflation by Winfield and lowered the scores of 30 students, with five going from a passing to a failing grade.

Winfield, who made $59,225 a year, refused to be interviewed by the OSI and submitted a letter of resignation on July 16, 2013.

The OSI concluded she improperly removed Regents exams from Chenault’s office, violated policy by grading her own students’ exams and inflated their scores.

She was unavailable for comment.

In another fixing case, Dorene Lorenzoni-Pericic, an assistant principal at Grover Cleveland HS in Ridgewood, Queens, submitted 11 grade-change requests to raise scores for one student from failing to passing.

Principal Denise Vittor reported the complaints to authorities on Oct. 6, 2014.

Lorenzoni-Pericic asked seven teachers in various subjects if they would sign off on a grade change for the student. All agreed, according to an April 7, 2015, report by the OSI.

She also signed off on two grade-change request forms on behalf of retired Science Assistant Principal John Pritchard, who was no longer at the school, according to the OSI report.

Lorenzoni-Pericic defended her actions to the OSI. She said it was her duty, on the principal’s orders, to review student transcripts to see “if anything can be done” to get students on track for graduation.

The student in question, identified as “Student A,” had special needs and had an individualized education plan that made him eligible to graduate with lower Regents exam scores, she said.

“She did not understand why this was an issue . . . She denied pressuring any teachers to change Student A’s grades,” said OSI prober Juliana Celik.

The OSI concluded, “The allegation that AP Lorenzoni-Pericic committed employee misconduct by improperly signing grade-change request forms, and by requesting that teachers sign and approve the grade-changer requests, for the purpose of giving Student A passing grades in 11 courses that he had failed is substantiated.”

The OSI also found Lorenzoni-Pericic engaged in misconduct by signing the retired Pritchard’s name on some of the grade-change request forms.

Lorenzoni-Pericic, who makes $126,306 a year, was reassigned out of the school in September 2015. She remains on the city payroll because her case is in limbo.

She is challenging the OSI’s findings of misconduct.

“I haven’t been accused of anything,” she told The Post outside her Queens home Monday.

“My hearing has not happened, yet. I’ve been waiting. I’ve been sitting for three years in the rubber room,” she said, referring to an office where educators are reassigned pending resolution of their disciplinary cases.

“The city says that doesn’t exist. I’m proof it does exist.”

Lorenzoni-Pericic then drove off in a black Mercury Mountaineer with Florida license plates.