Starting this fall, schools in Hong Kong will display colorful new government-issued posters declaring that “freedom comes with responsibilities.” Administrators may now call the police if anyone insults the Chinese national anthem on campus.

Students as young as kindergartners will be taught about a new national security law that gives the authorities the power to squelch opposition to Beijing with heavy prison sentences.

After months of antigovernment protests in Hong Kong, China’s ruling Communist Party is reaching into the semiautonomous territory to overhaul an education system that it sees as having given rise to a generation of rebellious youth. The sweeping law Beijing imposed earlier this month also targets Hong Kong’s students, who have been a galvanizing force behind the protests.

Carrie Lam, the city’s Beijing-backed leader, said at a forum on Saturday that the arrests of more than 3,000 children and teenagers at protests had exposed how the city’s campuses had been penetrated by forces hostile to the local and central governments.

“Faced with such a severe situation with our young people, we can’t help but ask, what is wrong with education in Hong Kong?” she said.

Mrs. Lam said the schools’ textbooks, classroom teaching and students’ extracurricular activities reflected negative news media reporting about China and the “wanton discrediting of the government and police.” Educating students about the new law, she said, would help them become more law-abiding.

The party’s goal for the territory is clear: to foster a new generation of loyal and patriotic Hong Kong youth. It is a strategy of ideological control that it has wielded to great effect in the mainland, but could rapidly erode Hong Kong’s reputation for academic freedom.

“Young kids will be brought up to understand and believe that without the Chinese Communist Party they have no future, that anything they have is because of the party,” said Steve Tsang, director of the China Institute at the School of Oriental and African Studies in London.

Over the last year, images of students in neatly pressed school uniforms joining hands to form human chains have become among the most evocative symbols of the protest movement.

But campuses have also been the site of some of the movement’s most violent scenes, such as at Polytechnic University, where protesters and police officers faced off in a prolonged fight with rubber bullets, firebombs and bows and arrows in November.

Now, in forcing through the security law, Beijing has signaled that it has seen enough. On Wednesday, Kevin Yeung, Hong Kong’s education secretary, barred students from singing “Glory to Hong Kong,” a popular protest song, displaying political slogans or forming human chains on campus.

Defenders of the law have argued that the city’s academic freedom would remain untouched. But, they say, students and teachers should know that freedom of speech comes with limitations.

“You can’t just allow teachers to talk, and impose their views, free for all,” said Regina Ip, a cabinet member who leads a pro-Beijing party in the legislature. “Critical thinking does not mean training people to criticize or attack.”

Even before the law was enacted, the transformation of Hong Kong’s education system was already underway.

The new school year had just started in September when Law Pei-lee, a teacher at a girls’ school, learned that a parent had filed a complaint about her conduct. She was accused of discussing the case of Lam Wing-kee, a local bookstore owner who was kidnapped by Chinese security officials in 2015.

Ms. Law, a veteran teacher, said she had mentioned the incident in passing. But she said the education bureau repeatedly demanded an explanation. Though she was never officially punished, she said the monthslong investigation felt like “psychological torture.”

Worse, Ms. Law said, she feared the law would stifle young minds. “Will our kids be able to think critically when they grow up?”

Both the education bureau and an employee at Ms. Law’s school, Sacred Heart Canossian School Private Section, said they could not comment on individual cases.

Some teachers and students say the investigations have created a climate of fear on campuses. A recent survey of more than 1,100 teachers found that around a third had been told by a supervisor to avoid discussing politics.

Some parents say they are only trying to keep their children out of harm’s way.

“What are the teachers afraid of?” said Ho Chiu Fai, a father of a fifth-grader and founder of Help Our Next Generation, a group of volunteers who investigate complaints against teachers. “We are all very worried that our kids will do something illegal, like go to illegal protests.”

Mr. Yeung, the education secretary, has vowed to “ferret out” problematic teachers. Leung Chun-ying, Hong Kong’s former top leader, has set up a fund to help investigate teachers.

“The Government have a duty to protect young minds from radicalization,” Mr. Leung wrote in an email.

Some teachers have lost their jobs for not taking a harder line against protest-related actions in school.

Lee Kwan-pui, a music teacher at Heung To Middle School, was fired in May after she let her students play “Glory to Hong Kong,” according to local media reports. Ms. Lee defended herself in an email she sent to the school’s staff and students, seen by The New York Times, saying she had reminded students to avoid social topics when choosing songs, but that ultimately it was their decision.

“I never brought up my political stance to students on campus,” she wrote.

After Ms. Lee’s firing, students formed human chains at the school in protest. Reached by telephone, an administrative employee at the school declined to comment.

The new national security law — which authorizes life imprisonment for secession, terrorism and other political offenses in the most serious cases — could make navigating classroom discussions even more difficult for teachers.

Liberal Studies, a mandatory civics course that has been blamed by some officials for radicalizing students, will likely come under much greater scrutiny. Chinese history has become a mandatory subject in middle schools, and some teachers have asked how they should discuss contentious events under the party’s rule.

Schools must review their library catalogs to remove books that “provoke any acts or activities which endanger national security,” the bureau said in a statement to The Times.

The law is already having a deterrent effect. At Ying Wa College, an elite boys’ school, a group of students who only last month chanted pro-independence slogans on the school’s sports field has now quickly disbanded and taken down its social media account.

Beijing’s broader push for control over the city’s schools and its sweeping interpretation of national security also raises questions about the future of Hong Kong’s status as a hub for higher education in the region.

The uncertainty over the law is driving concerns that scholars may be forced to censor themselves. Others fear that the vaguely defined crime of collusion could be applied to international academic collaborations.

Bruce Lui, a senior lecturer in journalism at Hong Kong Baptist University, pointed out the many topics that are covered by mainland China’s own national security law, ranging from the economy to outer space and, lately, biosecurity. Could researchers in Hong Kong, he asked, be punished for publishing data on the origins of the new coronavirus if their findings implicated China?

Some administrators are striking a defiant note. Kellee Tsai, the dean of the school of humanities and social science at the Hong Kong University of Science and Technology, encouraged her department to carry on their teaching and research as usual until further instructions were issued.

“There may well be non-obvious ‘red lines’ in Hong Kong’s higher education sector that cannot be crossed without severe legal consequences,” she told them in an email seen by The Times. “Let’s not draw those lines ourselves.”

Bella Huang contributed reporting.