A stunning 399 FDNY candidates who took the latest exam to join New York’s Bravest boosted their scores by claiming a parent or sibling died in the line of duty — but many of those claims are false, The Post found.

According to a just-released list of test-takers, 308 men and women who took the “open competitive” firefighter exam claimed a 10-point “legacy credit” as the child of a city firefighter, police officer or EMS worker who was either killed in the line of duty, died in the 9/11 terror attacks or succumbed to a 9/11-linked illness. Another 91 test-takers claimed the same credit as the sibling of such heroes.

And 16 of the 399 would-be firefighters claimed both a parent and a sibling who perished in service to the city.

It’s rare for a child or sibling of a fallen firefighter to join the Bravest. In recent years, biannual graduating FDNY classes of about 300 probies each have typically boasted one.

On 9/11, 343 firefighters and 23 NYPD cops lost their lives. As of last year, the FDNY and NYPD count a total 317 members who have died of 9/11-linked cancer and other illness.

The extraordinary number of test-takers with scores inflated by legacy credits suggests that many candidates wrongly claimed the credit, FDNY members said. Those scoring 100 and up are most likely to be hired in the next four years.

“If you lie that you lost someone on 9/11, you should be done,” a disgusted insider said.

Several top-scoring candidates are indeed the sons of deceased heroes.

Patrick Dowdell, received the highest score, 124 — ranking No. 1 on the list of 45,407 test-takers. His father, FDNY Lt. Kevin Dowdell, was killed on 9/11. The son received another 10-point credit as a disabled veteran — he served in combat as an Army captain in Afghanistan.

Robert Tilearcio Jr., 28, received a 113 score, ranking No. 18. His father, Robert Tilearcio, a veteran firefighter at Engine 266 in Far Rockaway, died last October of brain cancer linked to his 24-hour shifts on the Ground Zero pile, digging for victims. He was 58.

Tilecarcio, who took the firefighter exam two weeks before his dad died, did not claim the legacy credit at the time, he said, because it was made clear that the credit should go to offspring of the deceased.

“It’s not a tricky question,” Tilearcio told The Post. He requested and received the 10 legacy points after his dad’s death.

But some other applicants with scores over 100 admitted they don’t deserve the extra 10 to 20 legacy points they claimed.

“I thought it said, “Did you live through 9/11 and did it affect you?’ I was thinking that’s what that meant,” said Moriam Agoro, who received an impressive 113 score — ranking No. 5. She claimed a parent and sibling legacy for 20 extra points.

Agoro, 28 of Brooklyn, said she took an exam-prep course offered by the Vulcan Society, a fraternal group of black firefighters, which urged test-takers to grab extra points.

“They said click everything so you get all the credits,” she said. “They said if you didn’t get more than 100, [the FDNY] wouldn’t be calling you back, so you need all the extra points.”

Asked if the instructor explained what legacy means, Agoro said, “They didn’t explain none of those things for us.” A Vulcan rep could not be reached for comment.

Shannon Phillips, 25, got a high 115 score — ranking No. 7.

But she mistakenly claimed 20 extra points for a parent and sibling legacy. Her father and a brother are firefighters, but both are alive and well.

“I don’t know why they gave me those points,” she said.

Allison Bevers, who received a 103 score — ranking No. 765 — said her father is a retired firefighter and two brothers are active NYPD cops. She also claimed ignorance of the term “legacy.”

“I didn’t know what exactly that meant,” she said. “I’ve never taken a civil-service test. I don’t know how they go.”

The exam, administered last fall by the Department of Citywide Administrative Services, includes a section that lets test-takers check boxes for various credits. One line says: “I claim parent legacy credit.”

Another: “I claim sibling legacy credit.” Next to each line is a link to a description of who qualifies for the credits.

Ryan Solfaro, 26 of Staten ­Island, whose father is a cop and brother a firefighter, claimed the sibling legacy, telling The Post, “I read that as my brother is in the FDNY.”

“When the list came out, I had friends in the department contact me: ‘Is your brother OK?’ ” he said. Solfaro, whose score was 114 — ranking No. 8 — said he immediately e-mailed DCAS about his undeserved 10 points.

“I do hope they correct my list number to give more eligible applicants a chance to join New York’s Bravest,” he said.

DCAS did not verify the legacy credits before publishing the scores. A spokesman said the FDNY will do so.

“Any claims for credit … must be documented during the candidate-investigation process,” said FDNY spokesman Jim Long.

Additional reporting by Anna Sanders