Deng Yuwen, a prominent Chinese writer who now lives in exile in the suburbs of Philadelphia, has regularly criticized China and its authoritarian leader, Xi Jinping. China’s reaction of late has been severe, with crude and ominously personal attacks online.

A covert propaganda network linked to the country’s security services has barraged not just Mr. Deng but also his teenage daughter with sexually suggestive and threatening posts on popular social media platforms, according to researchers at both Clemson University and Meta, which owns Facebook and Instagram.

The content, posted by users with fake identities, has appeared in replies to Mr. Deng’s posts on X, the social platform, as well as the accounts of public schools in their community, where the daughter, who is 16, has been falsely portrayed as a drug user, an arsonist and a prostitute.

“I tried to delete these posts,” Mr. Deng said of the attacks online, speaking in Mandarin Chinese in an interview, “but I didn’t succeed, because today you try to delete and tomorrow they just switch to new accounts to leave attacking text and language.”

Vulgar comments targeting the girl have also shown up on community pages on Facebook and even sites like TripAdvisor; Patch, a community news platform; and Niche, a website that helps parents choose schools, according to the researchers.

The harassment fits a pattern of online intimidation that has raised alarms in Washington, as well as Canada and other countries where China’s attacks have become increasingly brazen. The campaign has included thousands of posts the researchers have linked to a network of social media accounts known as Spamouflage or Dragonbridge, an arm of the country’s vast propaganda apparatus.

China has long sought to discredit Chinese critics, but targeting a teenager in the United States is an escalation, said Darren Linvill, a founder of the Media Forensics Hub at Clemson, whose researchers documented the campaign against Mr. Deng. Federal law prohibits severe online harassment or threats, but that appears to be no deterrent to China’s efforts.

“There’s no question that this crosses a line that they hadn’t previously crossed,” Mr. Linvill said. “I think that suggests that the lines are becoming meaningless.”

China’s propaganda apparatus has also stepped up attacks against the United States more broadly, including efforts to discredit President Biden ahead of the presidential election in November.

“They’re exporting their repression efforts and human rights abuses — targeting, threatening and harassing those who dare question their legitimacy or authority even outside China, including right here in the U.S.,” Christopher A. Wray, the director of the Federal Bureau of Investigation, told the American Bar Association in Washington in April.

Mr. Wray said China was exerting “intense, almost Mafia-style pressure” to try to silence dissidents now living legally in the United States, including activities online and off, like posting fliers near their homes.

A spokesman for the Chinese Embassy in Washington, Liu Pengyu, said in a statement that he was not aware of the Deng case and had no comment. He added that the government’s State Council issued regulations in China last year to protect the safety of teenagers online.

In a statement, Meta said it had taken down Facebook accounts targeting the Dengs as part of its monitoring of Spamouflage’s activities. The statement said the activity hadn’t gained much traction on Facebook. Patch and Niche said they, too, had removed the accounts for violating their standards for use. X and TripAdvisor did not respond to requests for comment.

Not all the posts targeting the Dengs were removed, according to Mr. Linvill’s team at Clemson. New posts also continue to appear, and traces even of posts that are removed can linger online for years. Spamouflage’s attacks still appear in searches for Mr. Deng and his daughter on Google, for example.

The attacks from China have been a challenge for government and law enforcement officials in the United States. Last year, the Justice Department indicted 34 officers working for China’s Ministry of State Security on charges of harassing residents of the United States like Mr. Deng, but the officers live — and presumably continue to work — in China, outside the reach of American law enforcement.

Some have called for a more aggressive response, including Representative John Moolenaar of Michigan, the Republican chairman of the House Select Committee on the Communist Party of China.

“We need to educate and empower law enforcement officers and the American people to understand the C.C.P.’s tactics,” he said in a statement, referring to the party, “and protect the people seeking safe haven in our country.”

The Spamouflage network was first identified in 2019 during mass anti-Beijing protests in Hong Kong. It creates inauthentic accounts on social media or tech platforms to bombard actual users with spamlike content — hence the name researchers have given the network. While the content often fails to go viral, the swarming nature of the attacks can be a nuisance, or worse, for those targeted.

The network, which Meta last year linked to law enforcement agencies in China, once focused most of its attention domestically to discredit and intimidate critics of the Communist Party, like the protesters in Hong Kong.

It has become increasingly active abroad, seeking to influence political debates and elections in Taiwan, Canada and, since at least the 2022 midterm election, the United States. An American Olympic figure skater and her father, a former political refugee from China, were targeted by what the Justice Department described as a spying operation ordered by Beijing. Chinese journalists working abroad, especially women, have likewise been depicted in fake escort ads and faced bomb and rape threats.

The Justice Department indictment of the officers at the Ministry of State Security did not link them explicitly to the Spamouflage network, but the activities described mirror its work closely and appear “extremely likely” to be the same operation, according to a recent report by the Institute for Strategic Dialogue, a nonprofit research group. The institute also warned that the network was focusing increasingly on the American presidential election.

In Mr. Deng’s case, as with others, the intent seems to be to silence criticism. Mr. Deng, who was born in Xinyu, in southeastern China, once served as an assistant editor at Study Times, a weekly journal of the Central Party School of the Communist Party that trains rising officials.

His commentaries sometimes pushed the envelope of the party line. He was dismissed in 2013 after he wrote an opinion essay for The Financial Times — which appeared in its Chinese and English editions — calling for China to abandon its strategic ties with North Korea’s erratic authoritarian leader, Kim Jong-un. He eventually left the country.

Mr. Deng, who is 56, has lived in the United States with his wife and two children since 2018. He continues to publish essays in a variety of news outlets and books on Chinese politics and foreign policy. The latest book was “The Last Totalitarian,” published in Chinese in April by Bouden House in New York. In it, he argues that the Communist Party has lost the faith of the people and needs to reform.

In the interview, Mr. Deng said he was used to criticism from China’s officialdom, but the personal attacks began after he published an article in February in which he compared Mr. Xi’s cadre of top officials to the Gang of Four under Mao Zedong.

The first post that Clemson’s researchers spotted appeared that month on X, where Mr. Deng’s account has more than 100,000 followers. It mentioned a middle school in the family’s town and his daughter. The harassment spread to other accounts on X and then to numerous platforms, including Facebook, Medium, Pinterest, DeviantArt and Pixiv, a Japanese site for artists.

The posts denounced him as a traitor, a plagiarist and a tool of the United States. More than 5,700 posts to date on X alone have singled out his daughter, according to Clemson’s research.

The users’ profiles often made them appear to be American, though with few or even no followers. Many posts featured stilted, ungrammatical English, a signature of Spamouflage campaigns.

They became increasingly lurid and threatening. Doctored images appeared on Facebook with the face of Mr. Deng’s daughter superimposed on scantily clad women, advertising sex for $300. At least one post called for her to be sexually assaulted, offering a bounty of $8,000.

His daughter, who speaks English with a teenager’s fluency in Gen Z slang, was initially angry about the attacks, as well, Mr. Deng said, but at his encouragement, she has also tried to shrug them off. “I want to try my best not to get my family involved in my affairs,” he said.

Meta, Google and other major tech platforms have long been aware of Spamouflage’s activities and have sought to blunt their reach. Last year, Meta announced that it had removed more than 7,700 fake accounts on Facebook linked to the network in one quarter alone.

Mr. Linvill of Clemson said China’s tactics were likely to continue because the country had “yet to face any meaningful repercussions beyond accounts’ being taken down, and that is no cost at all from their perspective.”