A good part what would form the northern part of the Town of Lansingburgh was annexed in 1819 from Schaghticoke. North Lansingburgh, as the part of the town above the village was sometimes called, encompassed Speigletown, Hogle City, Grant’s Hollow (at least that portion south of the Deep Kill), Rice Mountain, Thieves Hollow, Campbell Island (not to be confused with the one at Schodack), and the areas now called Pleasantdale, Valley View Park, and Sunset Heights. The annexation was not universally desired, as witness a remonstance to the New York State Assembly opposing it, but there seems not to have been any lasting objections to having been removed from the Town of Schaghticoke.

There were at least a few attempts to make at least some part of the area of northern Lansingburgh into a new town. The first seems to have been one in 1850, with apparently no name mentioned for the proposed town. The second seems to have been in 1866 when there was an attempt to create the Town of Lincoln. The third (and last?) seems to have have been one in 1879 when there was an attempt to create the Town of North Lansingburgh. While the attempts may have had something to do with the more rural area having different politics or different needs than the Village of Lansingburgh, it may also have had something to do with adding additional supervisors from towns to the Rensselaer County Board of Supervisors so that they would continue to outnumber the number of supervisors representing wards of the City of Troy.

The area of northern Lansingburgh became part of the Town of Schaghticoke again in 1901, following the bills that annexed the Village of Lansingburgh to the City of Troy and otherwise dissolved the Town of Lansingburgh.

Taken from the LANSINGBURGH TOWN BOOK:
AT A SPECIAL TOWN MEETING OF THE FREEHOLDERS AND INHABITANTS OF LANSINGBURGH duly waived & notified according to the Statute in such case made & provided held at the house of Adolphus Walbridge, Innkeeper in the town of Lansingburgh on the 11th day of January 1819, at 11 o’clock in the forenoon..
For the purpose of taking into consideration an application of the Freeholders, & Inhabitants of the Town of Schaghticoke to the Legislature of the State of New York for the annexation of a part of the said Town of Schaghticoke viz:
All that part of the said Town lying south of the Diepe Kill to the Town of Lansingburgh.–
It was resolved on motion that a Committee of Five persons be appointed to meet with a committee from that part of Schaghticoke proposed to be annexed to this town and that the said Committee be Cornelius Lansing, Levi Coley, Elias Parmelee, Samuel Bontecou & Calvin Barker & that the said Committee inquire & report facts- connected with the said application on the 18th day of January instant at 1 o’clock P.M. at this place to- which time & place this meeting is adjourned.
Monday January 18th, 1819, 1 o’clock P.M. Met pursuant to adjournment, the report of the Committee was read to the meeting whereupon resolved that the question of the said application be taken by ballot and the meeting proceeded to balloting, and on counting the ballots there was a majority in favor of the annexation of that part of the Town of Schaghticoke lying south of the Diepe Kill to the Town of Lansingburgh. adjourned.

Legislature of New-York
—
IN ASSEMBLY
Tuesday, February 23.
Petitions, &c.—[…] Remonstrance of sundry inhabitants of the town of Schaghticoke, against being annexed to the town of Lansingburgh.
Albany Argus. February 26, 1819: 2 col 5.
Rochester Telegraph. March 8, 1819: 2 col 3.

AN ACT to annex a Part of the Town of Schaghticoke to the Town of Lansingburgh, in the County of Rensselaer.
Passed March 26, 1819.
I. BE it enacted by the people of the State of New-York, represented in Senate and Assembly, That so much of the town of Schaghticoke, in the county of Rensselaer, as is bounded on the west by Hudson’s river, on the north by a line commencing at the mouth of a brook called Deepy-kill, and running along the middle of said brook in an easterly direction, until it intersects the western line of the town of Pittstown; thence along the said western line of the town of Pittstown, to the town of Brunswick; thence along the north line of said town of Brunswick to the said town of Lansingburgh, be, and hereby is annexed to the town of Lansingburgh.
II. And be it further enacted, That from and after the passing of this act, the said town of Lansinghurgh, together with the before mentioned part of the said town of Schaghticoke, shall be and remain a town by the name of Lansingburgh ; and that the remaining part of the town of Schaghticoke be, and remain a separate town by the name of Schahgticoke.
III. And be it further enacted, That as soon as conveniently may be, after the passing of this act, the supervisors and overseers of the poor of the towns of Schaghticoke and Lansinghburgh aforesaid, shall, pursuant to notice to be given by the supervisors of the towns last aforesaid, for that purpose meet together, and apportion the poor maintained, at the time of the passing of this act, by the town of Schaghticoke, and also divide all the money which is, or may be, in the hands of the overseers of the poor of the said town of Schaghticoke, in an equitable manner ; and if the supervisors and overseers of the poor aforesaid cannot agree upon such division, then the supervisors of the county, at their next annual meeting, shall apportion the poor and money between the said towns of Schaghticoke and Lansingburgh, in an equitable manner as aforesaid.
And whereas, It appears that the said town of Lansingburgh has heretofore raised the sum of five hundred dollars, as a fund towards the building a poor house, which remains now on hand ; Therefore,
IV. Be it further enacted, That the assessors of the town of Lansingburgh be, and are hereby further authorised, at the next assessment of the said town, to add on to the assessment of the inhabitants living in that part of the said town of Schaghticoke, hereby annexed to the said town of Lansingburgh, the sum of eighty-five dollars, being the proportional sum they ought to raise for building a poor house as aforesaid.
Laws of the State of New-York. Albany, NY: William Gould & Co., 1821. 83-84. https://books.google.com/books?id=s0IwAQAAMAAJ&pg=PA83

In March, 1819, a strip of land across the S. end of this town was annexed to Lansingburgh, bounded N. by Deepy Kill, a small brook, now the line between this town and Lansingburgh, the transferred territory being, as near as I can find out, about 2 miles wide.
Spafford, Horatio Gates. A Gazetteer of the State of New-York. Albany, NY: B. D. Packard, 1824. 473. https://books.google.com/books?id=tw9IAQAAMAAJ&pg=PA473