There are an estimated 3,500 homeless veterans in New York City, and some of them will soon have a new place to seek shelter. Construction on a new facility in the Kingsbridge area of the Bronx, which will house 76 formerly homeless and low-income veterans, broke ground yesterday. The building, at 2701 Kingsbridge Terrace, is being built by Jericho Project, a group that works to find solutions to homelessness. Jericho Project is also overseeing another new residence for veterans at 355 East 194th Street, though the group said its efforts barely make a dent in the need for such projects. When the Kingsbridge Terrace residence opens in 2011, priority will be given to local, low-income veterans who are returning from Iraq or Afghanistan, and the rest will be open to any veteran with a history of homelessness or substance abuse. A $1 million grant for the project was provided by Bronx Borough President Ruben Diaz, allocated for green roof and energy-efficient systems and appliances.