WASHINGTON — Rep. Elise Stefanik, 30, the young­est woman ever elected to the House, has already had several run-ins with congressional staffers and security personnel who can’t believe someone that young is really a lawmaker.

The trouble began when staffers showed newly elected legislators around their new digs.

“The first time they brought the freshmen onto the floor for orientation they said, ‘Staff?’ I shook my head no. They said, ‘Spouse?’ I shook my head no. They said, ‘Member?’

“‘Yes,’ ” Stefanik told The Post.

In a similar incident, the upstate New Yorker walked down the Capitol steps, where the public is no longer allowed to gather, and a Capitol police officer demanded her ID to make sure she was a member of Congress.

Stefanik laughed about the encounter Tuesday, when she was sworn in as one of the most-watched members of the new Congress. She shattered a four-decade record held by another New Yorker, Elizabeth Holtzman, who was 31 when she took office in 1973.

Now that she’s a full-fledged lawmaker, Stefanik gets to wear a small pin that will signify her status and allow her to breeze through security.

Still, Stefanik stood out Tuesday among the 434 members who took their oaths on the House floor, sporting a bright blue dress that contrasted with the dull hues dominating the chamber. Some fellow Republican women opted for bright red power suits.

Stefanik’s first official act was voicing support for John Boehner as speaker of the House.

There are 52 new House members and 12 new senators in the 114th Congress. A record 107 women are now serving.

Stefanik won her seat by defeating Democrat Aaron Woolf in an upstate district that runs from Saratoga County to the Canadian border and which was previously held by Democrat Bill Owens.

Republican Party leaders, in a sign of Stefanik’s promise, put the former Bush administration staffer on the influential Armed Services Committee.

Stefanik appeared a bit frazzled as she tried to corral family members and make it to an official photo session on time after her swearing-in.

“I’m just trying to figure out where I’m going, guys,” she told reporters as she at first tried to avoid questions, then gamely took a few.

“It was just an amazing experience to take the oath of office,” she said. “I’m just so excited to be here.”