In particular, some have worried that the bill would restrict Boy Scouts and other children who learn to shoot at summer camp or as part of trap teams. The bill applies not only in the gun owner’s home but anywhere that a child might have access to the weapon.

The bill makes exceptions for children under 16 who have a hunting license, but children learning to shoot at camp often do not have a license. Under New York law, children between 12 and 15 may shoot guns at a range under adult supervision.

Patrick J. Morse, the founder of the group North Country Friends of the Second Amendment, said those children’s experiences qualified them to be around guns, despite their age.

“We have people on our trap team who are 12 years old, and they know everything there is to know about a gun,” he said. “You have other places where someone is 25 years old and has never seen a firearm.”

A more sensible law would require guns to be kept away from untrained people, rather than people under a certain age, Mr. Morse said.

Ms. Paulin acknowledged the potential issue and said she would be open to amending the bill. “It’s a good point. Those programs are very successful, and a lot of people in the state participate in them,” she said .

“We’re absolutely looking at it seriously,” she said. “The Boy Scout problem is solvable.”

Others opponents have cited enforcement and constitutionality as roadblocks.