Eulogia was scared and adrift. At 25, she was poor, pregnant and an illegal immigrant. She worried about how she would pay for medical care and raise her baby, and even whether a trip to the hospital might prompt her deportation to Mexico.

But when she plunged into a postpartum depression in 2003 after the birth of her daughter, the first of three children, a hospital social worker referred her and her husband to an East Harlem social service agency that has counseled them and helped them get care for their family and get the government assistance their children were eligible for as American citizens.

“I think I very am lucky,” Eulogia said in an interview this week, asking that her last name not be used because she still fears deportation. She said most illegal immigrant parents felt tremendously isolated and did not have “the confidence to ask for help.”

Indeed, a recently published study of the early development of children born to illegal immigrants in New York City suggests that most stories that begin like Eulogia’s do not end as well.

Even though the children have citizenship and live in an immigrant-friendly city that offers them a wide array of services, many are still hobbled by serious developmental and educational deficits resulting from their parents’ lives in the shadows, according to the study, whose author says it is the most comprehensive look to date at the effects of parents’ immigration status on young children.

“The undocumented are viewed in current policy debates as lawbreakers, laborers or victims — seldom as parents raising citizen children,” wrote the author, Hirokazu Yoshikawa, a Harvard education professor who has published the study as a book, “Immigrants Raising Citizens” (Russell Sage Foundation, 2011).

Professor Yoshikawa found that by the time the children of illegal immigrants reached age 2, they showed significantly lower levels of language and cognitive development than the children of legal immigrants and native-born parents.

“Millions of the youngest citizens in the United States, simply by virtue of being born to a parent with a particular legal status, have less access to the learning opportunities that are the building blocks of adult productivity,” he wrote.

The implications for the nation are potentially far-reaching and long-lasting, he said, considering that of all preschool children of illegal immigrant parents in the United States, an estimated 91 percent — four million children — are American citizens.

Poor cognitive development can lead to lower school performance, which in turn can lead to higher dropout rates, an undertrained work force and lower economic productivity. “Ignoring these children has costs for society,” Professor Yoshikawa warned.

He and his team began their research by visiting maternity wards at public hospitals around New York in 2004 and getting permission to study nearly 400 babies newly born to Chinese, Dominican and Mexican parents, as well as to native-born African American parents. The researchers, who were affiliated with the Center for Research on Culture, Development and Education at New York University, followed the children for three years.

The researchers found that poor immigrants cannot afford learning materials or stimulating programs in child care centers. Fear of deportation or ignorance about how the city works often prevents those parents from seeking help from government agencies that provide child care subsidies or food stamps.

Many illegal immigrants, particularly those belonging to newer immigrant groups, like Mexicans in New York, have smaller extended families or less-developed social networks than others, and therefore fewer people around to help raise children.

The psychological stress suffered by illegal immigrants — many of whom work long hours for low wages and live in crowded, poorly maintained apartments — can be transmitted to young children, the study says.

“Greater hardship among parents, both economic and psychological,” Professor Yoshikawa wrote, “can harm children’s learning by lowering parents’ active engagement with their children, the quantity or quality of their language or their warmth and responsiveness.”

In an interview, he pointed out that   illegal immigrants’ anxieties about seeking help — and those anxieties’ effects on children — could be even worse in places with “harsher” immigration policies.

Eulogia, the East Harlem mother, said she was brought to the United States by her parents when she was 11 and lived in a succession of cramped apartments in New York. She helped her parents sell flowers on the street to make ends meet. Though she graduated from high school, she remained an illegal immigrant, and imagined that her own children would live the same kind of existence.

Little Sisters of the Assumption Family Health Service — a community-based organization in East Harlem that provides counseling and other assistance to poor people, especially immigrants — helped Eulogia and her husband get food stamps and enroll in the federal Women, Infants and Children assistance program. Her eldest daughter, now 7, receives after-school tutoring at the center, while her second child, a 2-year-old boy, is getting speech therapy. And the family has secured better housing.

In his book, Professor Yoshikawa extols the work of groups like Family Health Service.

“By bringing these families out of the shadows and providing them with access to better work conditions and learning opportunities,” he wrote, “we can ensure that the nation’s most vulnerable young citizens have an equal chance to succeed in their early development, later schooling and adulthood.”