I am descended from Henry Bauer (b. 1863), son of Jacob and Magdalene Bauer (Jacob b. 1830/1831).
According to Jacob's information, he was born in NY (lived in the Orangeville area mostly and died in the poorhouse in Varysburg in 1921). According to his documentation, his father was born in France.
The 1850 Census for Wyoming county, Orangeville NY lists
Frederick Bower 59
Ellen Bower 51
Frederick Bower Jr. 21
Jacob Bower 19
Geo Bower 16
Henry Bower 12
This matches other info of a Frederick Bauer b. 1792 in France and having a son Frederick in France in 1828. Since the next born in Jacob and he lists his birth as NY its reasonable to believe Frederick, his wife and son Frederick immigrated in either 1828, 1829, or 1830, had Jacob, George, and Henry in NY.
The 1860 Census in Wyoming county, Orangeville, NY lists
George Bauer 26
Ellen Bauer 30
Lana Bauer 4
Josephine Bauer 2
George Bauer 11 months
Frederick Bauer 68
Lana Bauer 61
So it's reasonable to believe Frederick Jr., the son from the 1850 census, married, had kids, and his parents moved in with them and were recorded there for the 1860 census.
Also, there is an obit in an Attica newspaper for a Magdalene's death in 1907 and she's the wife of George Bauer (many people in the same pool of the family had similar names. Especially Magdalene/Magdalena. Some kept the full name, other's shortened it to Ellen, Lana, Lena, and even Madeline. This has made it quite difficult to put together the family tree with correct names and dates and marriages.) This Magdalene, maiden name Sattler (b. 1830), who married George Bauer (b.1834) and she died in the home of her daughter, Mrs. Frank Shoeder. It was the daughter Josephine that married Frank Shroder.