Adamsville was a name of the northeastern or northern part of the Village of Lansingburgh.
James J. [I.] Adams, an old and esteemed citizen, died at his residence, in the village, a few days ago. He represented the town in the Board of Supervisors several years. His name is identified with the prosperity of the village by reason of his connection with Mr. A. A. Peebles, and purchasing the property in the north part of the village—now known as Adamsville—and laying it out in village lots, which has grown to become a most thriving and important part of the village. His last efforts were in connection with Messrs. Vail, Whipple & Peebles, in the purchase of the Lansing farm, through which the new avenue runs, and laying them out also in village lots since which time declining health has prevented further activity.
Troy Daily Whig. January 12, 1867: 1 col 2.
Baxterville seems to have been another name for the area, or part of it. A Charles Baxter lived in the Oil Mill Hill area and had been one of the opponents in 1869 of an attempt by Troy to annex Lansingburgh.
FOR SALE […] a dwelling house 2 stories high, and one 1 1/2 stories high, situated at the foot of Oil Mill Hill in Baxterville, with an unexpired lease of about 60 acres of land. Troy Daily Whig. August 9, 1844: 3 col 3.
An Adamsville Community Association formed in 1925 existed until at least 1929, and opened an Adamsville Playground on Oil Mill Hill.