Actual college savings, if families do not add money to the funds, will be slight: With only the $100 initial contribution and $200 in matching funds, assuming a 4.5 percent annual return, the child’s account would be worth about $475 after 12 years.

Champions of child savings accounts, however, argue that they have an impact beyond a simple financial one, by encouraging parents to believe that their children can go to college.

Since most child savings account programs are relatively new, research on their effects is just beginning. A randomized controlled trial of mothers and infants in Oklahoma, in which some infants were selected to receive $1,000 in a 529 account, along with incentives for the mother to save additional money, found that those disadvantaged children scored better at age 4 on a measure of socioemotional development than similar children who did not receive the money. Three years after the study began, mothers of infants who received the money also showed fewer symptoms of depression.

William Elliott, an associate professor and director of the Center on Assets, Education and Inclusion at the University of Kansas, said child savings accounts had many potential financial benefits.

“If you have savings early on, you’re more likely to be connected to financial institutions later in life,” he said. “You’re more likely to buy stocks, invest in real estate, buy a home, do the things that build assets.”

The Office of Financial Empowerment at the Department of Consumer Affairs runs centers across the city that offer free financial counseling. The department plans to use the centers in the chosen school district to educate families about 529 accounts, as well as help them set up their own.

More than 800,000 New Yorkers do not even have bank accounts, Ms. Menin said. She said she hoped that the program would have a ripple effect in connecting families with financial institutions.