William Foster b. 1808 or 1817/1818 New York City, New York. His parents are unknown.
There is the possibility that he was the boy that was left as an orphan and ended up in New York City Almshouse in 1818.
Source: New York, New York, US. Almshouse Ledgers
1758-1952
1818 William Foster 10 years old (b. 1808)
This could be reason why I have never been able to find his parents if this is my great grandfather?

1860 Census says William Foster b. "New York", and his 1st wife Mandana Townsend and Stoughton ancestors came from New York to Cincinnati, Hamilton Co., Ohio. His first born by 1/wife Mandana Townsend was Edwin Ruthvan Foster and he says: "he was born New York". William Foster left New York as young adult and in 1836 living Cincinnati, Hamilton Co., Ohio. William Foster lived in Wheeling, Ohio Co., West Virginia, Cincinnati, Hamilton Co., Ohio and Oquawka, Henderson Co., IL. Children from 1st marriage were born in Evansville, Vanderburg Co., Indiana, Wheeling, WVA and Cincinnati area. He worked along the Ohio River as engineer (probably a River Boat Engineer or Mechanic) as stated 1850 Federal Census Oquawka, IL., which I think it meant "boat engineer" in his case and not railroad engineer.

1/w Mandana Townsend d/o Epenetus Townsend and Polly Stoughton of Putnam, Muskingum Co., Ohio and Hamilton Co., Ohio. Stoughton line goes back to New York. William Foster and Mandana Townsend married 4 Feb. 1836 Hamilton Co., Ohio.

Daughter by his 2nd wife Elizabeth Ellen Lathrop Foster, Viola Foster LaDow indicated in paper to my mother that William Foster b. 1808 New York but Census records 1850, 1860, 1870 says born 1817 New York. The 1870 Census would be before June 1817.

Children by 1/wife Mandana Townsend were:
1. Edwin Ruthvan Foster m. 1/w Sarah E. Maley (1st cousins)
2/w Mrs.Grata Callista(Phillips)Speris
3/w Mrs. Sarah L. (McFadden) Mickel
(died and buried Ionia, MI., Illinois Civil War tomebstone)
2. Elizabeth Foster m. 1/h Clement F. Briery
2/h Edgar E. Ladu
(died and buried in Sutter Co., CA.) pauper grave

3. Mary Matilda Foster m. Charles Robert Smith
(died and buried Los Angeles, CA.)

4. Sophia Foster m. 1/h Julius Gifford (Sheriff of Oquawka, IL.)
2/h Albert Warren
(died and buried Chicago, Cook Co., IL.)

5. "Carrie" Caroline Foster m. Abel Briggs
(died and buried Oakland, Alameda Co., CA.)

His 2/wife was Elizabeth Ellen Lathrop d/o Elijah B. (Bogue) Lathrop and Sarah A. Munson of Henderson Co., Il. Married 15 Feb.1860 Oquawka, Henderson Co.,IL. to William Foster.
Children by 2nd wife:
1. George T. Foster
2. Cora Ann Foster
3. Viola Captola Foster
4. Olie May Foster
5. Frank Foster (my grandfather)
6. Hattie M. Foster
7. Sarah Hazel Foster
8. Lucy J. Foster
9. William M. Foster aka. William H. Brown raised by (James) Homer Brown
and Catherine Mickel, Fortner, Brown. He changed name prior to 1900 to
William H. Brown.

1850 Federal Census, Oquawka, IL. occupation Engineer. (probably boat engineer and not train) later 1860 Census's he was a house painter with oldest son Edwin Ruthvan Foster.
William Foster buried in Oquawka Cemetery next to 1/wife Mandana Townsend Foster. No tombstone found in county. Old Section plot 194. First burials were in 1834 in this cemetery.

Federal Census
1840 Wheeling, Ohio Co., West Virginia then Virginia or Evansville, Vanderburg Co., IN.
or county along the Ohio River.

1850 Oquawka, Henderson Co., IL.
William Foster age 33 Engineer New York
Mandana Foster 32 Ohio
Edwin Foster 12 New York
Elisabeth Foster 10 Virginia
Mary M. Foster 8 Indiana
Sophia Foster 6 Indiana
Caroline Foster 8/12 Kentucky

1860 Oquawka, Henderson Co., IL. P.O. Oquawka
William Foster age 43 Painter b. New York
Elizabeth L. Foster 16 b. IL. (2nd wife Elizabeth Ellen Lathrop )
Caroline Foster 10 b. IL
Wedin Spartz 21 Laborer b. IN
Stephen Taylor 24 Pikes Peakel b. IN
Edward Hammon 23 " " b. IN

1870 Oquawka, Henderson Co., IL.
William Foster age 56 Painter b. New York
Ellen Foster 23 Keeping house b. IL ( 2nd wife)
George Foster 9 b,IL
Sophia Foster 8 b. IL (Cora A. Foster)
Tuny Foster 6 b. IL (Viola C. Foster)
Deborah Foster 4 b. IL (Olie Foster)
Frank Foster 1 b.IL (my grandfather Frank Foster)

OBITUARY
Thursday 6 March 1879 "Oquawka Spectator"
Mr. William Foster, who has been a resident of Oquawka for many years died at his home on Tuesday. He had been laid up with rheumatism for nearly a year.

William Foster and 2/w Elizabeth Ellen Lathrop Foster were my great-grandparents. Their son Frank Foster m. 2/w Elfa Rose Babcock were my grandparents. I was very close to my Grandmother Elfa Rose (Babcock) Foster, Monks since she lived with us growing up in San Bernardino, CA. Frank Foster buried in White Cloud, MI., where son Glenn Dewey Foster buried. Grandma Elfa Foster, Monks buried in Fairplains Cemetery, Grand Rapids, MI., with second husband Herbert Monks.