BEIJING — Cheng Nan has spent years trying to ensure that her 16-year-old daughter gets into a college near their home in Nanjing, an affluent city in eastern China. She wakes her at 5:30 a.m. to study math and Chinese poetry and packs her schedule so tightly that she has only 20 days of summer vacation.

So when officials announced a plan to admit more students from impoverished regions and fewer from Nanjing to local universities, Ms. Cheng was furious. She joined more than 1,000 parents to protest outside government offices, chanting slogans like “Fairness in education!” and demanding a meeting with the provincial governor.

“Why should they eat from our bowls?” Ms. Cheng, 46, an art editor at a newspaper, said in an interview. “We are just as hard-working as other families.”

Parents in at least two dozen Chinese cities have taken to the streets in recent weeks to denounce a government effort to expand access to higher education for students from less developed regions. The unusually fierce backlash is testing the Communist Party’s ability to manage class conflict, as well as the political acumen of its leader, Xi Jinping.