Google Legume or Leguminosae - these plants are considered nitrogen fixers.
If you have or developing a forested - shady garden area, consider planting a Yellowood tree - Cladrastis lutea. Other trees of this Genus are Redbud, Black Locust, Honey Locust, and Kentucky Coffee Tree.
I put trees down as you indicate that you are beginning a forested area in your yard.

If you would like nitrogen-fixeing shrub native to New York: buffaloberry (Shepherdia spp.); go with Shepherdia argentea, as the berries are better tasting.

Btw, most of the plants krazyaroider recommends are: non-native (to NY); invasive; and one is not even a nitrogen-fixer: redbud (that's a tricky one, since it is in the bean/legume family).

If you'd like a tree that is nitrogen-fixing, choose a variety of native alder (Alnus spp.)

Btw, keep in mind: buffaloberry is native to the midwest - AND TO NEW YORK - look up the distribution range maps (google: [the plant] + usda).. (...or pollen library)