This is a shingling hatchet–it could trim wood, serve as a hammer, and the notch could remove nails. (The shingles would have been wooden ones.)

It is marked “Underhill Edge Tool Co.” Underhill Edge Tools was founded by George Underhill in 1852 in New Hampshire. There were several companies that merged throughout the 1800s, and this name was probably not used after 1890. There may have been Underhills making tools in New Hampshire as early as the late 1700s.

Some sources call this a carpenter’s hatchet, and you can find a few YouTube videos about using this type of hatchet for any small wood-shaping task, such as trimming pieces to make camp furniture.

(Illustration from A Museum of Early American Tools by Eric Sloane)