Nationwide, state laws require a municipality to designate one print publication each year as its official paper to handle these notices. But increasingly, many state lawmakers across the country have been calling for the notices to be posted for free on government websites, instead of in print papers.

In 2018, at least 88 bills were introduced to eliminate or reduce the use of printed public notices, most of which did not pass, said Richard Karpel, executive director of the Public Notice Resource Center, who added that the number of such bills has risen in recent years.

Many were sponsored or supported by elected officials with testy relationships with the media, Mr. Karpel said, including the former Republican governors Chris Christie of New Jersey and Paul LePage of Maine.

“Eliminating newspaper notices would cripple many newspapers,” Mr. Karpel said. “It would reduce the already shrinking profit margins of most large papers and newspaper chains, and it would completely obliterate smaller newspapers, especially those that publish in rural areas.”

There are plenty of examples of government officials using the notices to try to strong-arm newspapers over their coverage.

Richard Abel, publisher of the The Westmore News, which publishes two paid weekly newspapers north of New York City in Westchester County, said an official from the Village of Rye Brook threatened to divert its public notices and asked officials in neighboring municipalities to do the same, unless he fired a critical columnist. Mr. Abel refused and ran a column scolding the officials for trying to squash them “via economic sanctions.” The villages never pulled the ads, he said.

Ms. Norris said her advertising revenue comes largely from print ads from real estate agents and other local businesses. Still, though the notices account for a much smaller fraction, the motive behind pulling them was vindictive and troubling, she said.

She wrote an article under the headline “Mayor: Village may cut off information to News,” and in an editorial, called the change an attempt to censor her coverage and vowed that the paper would not back down.

In a publisher’s column last month, she wrote a piece called “The Empire Strikes Back” and accused the board of trying “to use the power of their offices and your tax money to try to do something unconscionable — muzzle criticism of their actions in this newspaper” by “cutting off the various columns and press releases from all parts of the village, so that we couldn’t bring that information to you.”

Ms. Norris said there has been a notable rise in opposition to her coverage of Village Hall since Mr. Trump entered the White House.

After a meeting in August where someone shouted “fake news” after the mention of her paper, she wrote an editorial — “It Trickles Down” — decrying the Trump administration’s attempt “to marginalize the news media.”

“Even here in Garden City we’ve encountered echoes of it,” she wrote, adding that, “The tenor of the local debate seems to also reflect the extreme polarization that we’ve seen nationally.”

Dave Gil de Rubio, editor of The Life, said that he welcomed getting the notices, especially since the newspaper, founded in 1985, has sometimes been regarded as “the little stepbrother to The News.”