But when she found out that she did not qualify, she contacted Mr. Cuomo’s office and was routed to the state’s Higher Education Services Corporation, the state’s student financial aid agency. It was to no avail, according to email correspondence she shared with The New York Times.

“Among others, continuous enrollment is a criterion for Excelsior Scholarship eligibility,” one email read. “Due to your break in schooling, you are not eligible for the program. Sincerely, Correspondence Unit.”

“You’re kind of beat up, you’re kind of distraught,” Ms. Frenkel said of her response.

The program is the first in the country offering tuition help for students at two and four-year public schools. As a “last dollar” program, it comes into play after other scholarships and grants — such as federal Pell grants or the state’s generous Tuition Assistance Program, both of which go the lowest-income students — are already taken into account. State officials note that more than 40 percent of applicants to the tuition program are denied.

Yet New York’s program differs in several ways from others aimed only at community college students. While Tennessee took several months to develop its program, New York has rolled out its endeavor with remarkable speed, from the initial proposal in January to passage by the Legislature in April, to the release of formal guidelines in May and the start of applications, in June.

The program is expected to slice the cost of a degree from a four-year SUNY school — now almost $83,000 for tuition, fees, room and board — by about $26,000. Critics have said that making it a tuition-only award penalizes the poorest students, who often need help with living expenses, books and fees that are not covered by Excelsior.

Though it is still too early to tell what effect the scholarships will have on how New York students choose colleges, CUNY reported last month that freshman applications increased 9 percent this year to a record 76,000, and attributed some of that surge to the Excelsior program.