Sensored Life, for example, in Penn Yan, moved one mile to qualify for the program: from a spot on the village’s Main Street to a business park owned by a county development agency, which leases space to Keuka College, a Finger Lakes school.

Sensored Life, which sells automated home-monitoring equipment, has promised to hire 17 people and invest $140,000 over the next several years. But it has three employees at the moment, including a co-founder, Michael O’Brien, a 63-year-old entrepreneur whose previous start-ups have included companies that made lacrosse goals and a slip-resistant footwear.

Mr. O’Brien said that he had not yet sold “a heck of a lot” of his newest product — the MarCell, a temperature, humidity, water and power monitor — but that he was a big fan of Start-Up New York, which exempts him from paying state sales and income taxes.

“We’re a small business at this point,” he said, “but we have high hopes.”

Start-Up New York was one of Mr. Cuomo’s marquee projects in his first term as governor, born out of his desire to create and keep jobs in New York, among the states with the highest taxes.

The program’s beginning set high expectations. At one point Mr. Cuomo, a Democrat, said that Start-Up New York would be “the greatest economic savior” for upstate. At another point, a Start-Up official suggested that the governor wanted the program to create up to 10,000 jobs a year, although the official later clarified that the figure referred to the annual cap of how many jobs could qualify under the program.

Mr. Cuomo’s confidence in the program has been unshakable. Since late 2013, the state government has advertised Start-Up New York nationwide, spending $46.9 million to promote it between December 2013 to March 2015, according to the Empire State Development Corporation, the government agency that administers the program.