Kateri,

Perhaps you have found much of this since your post, but below is what I found.

Despite the oral history that Jacob was a "stowaway," according to both the 1900 and 1910 censuses, he immigrated c. 1880, and a likely match is:

New York Passenger Lists, 1820-1957 > 1881 > July > 27 > Henry Edge
Ship Henry Edge sailed Antwerp arr NYC 27 July 1881
Sheet 1 line 37
Jacob Muth 27y male farmer from Germany to USA in steerage

Perhaps the fact that he traveled in "steerage" evolved across the years to "stowaway"?

His census entries indicate that he was naturalized in 1885. You could obtain his naturalization papers from Oneida county.

Regards,
Susan Bork
Little Falls, NY
============

1900 United States Federal Census > New York > Oneida > Verona > District 92
13 June sh 6A beg ln 5 dw 124 fam 127
Jacob Muth head Dec 1856 md 17y GER GER GER imm 1880 here 20y nat’d farmer owns farm #63 on schedule w/mtg
Rosena wife June 1858 md 17y mother of 2/2 living NY GER GER
Fred P. son June 1882 NY GER NY NY GER NY
Charles H. son May 1893

1910 United States Federal Census > New York > Oneida > Verona > District 167
29 Apr sh (?)8A beg ln 2 dw 144 fam 154
Jacob Muth head 56 md 1x md 29y GER/Ger GER/Ger GER/Ger imm 1880 nat’d spks Eng farmer/general farm (wks own acct) farm owns farm #94 on schedule free of mtg
Rose wife 55 md 1x md 29y mother 2/2 living NY GER/Ger GER/Ger spks English
Charles A. son 16 single NY GER/Ger NY spks Eng laborer/home farm wage
Ln 5 dw 145 fam 155
Fred P. Muth head 27 md 1x md 6y NY GER/Ger NY spks Eng farmer/farm wks own acct owns farm #95 on schedule w/mtg
Mamie wife 26 md 1x md 6y mother of 2/1 living NY NY NY spks Eng
Ethel M. dau 5 single NY NY NY

1920 United States Federal Census > New York > Oneida > Verona > 189
6 Jany sh 2A beg ln 20 farm dw 32 fam 34
Charles A. Muth head owns farm 26 single NY HESSE DARMSTADT/Ger GER/Ger farmer/dairy farm wks own acct farm #12 on schedule
Jacob father 65 wid imm 1880 nat’d 1885 HESSE DARMSTADT/Ger GER/Ger GER/Ger farmer/dairy farm wks own acct

1920 United States Federal Census > New York > Oneida > Rome > District 92
21 Jany sh 1B bg ln 93 dw 18 fam 26
114 (James) St.
Frederick head 36 NY GER/Ger NY shipping cleark/wire mill
Mamie wife 34 NY NY NY
Ethel dau 14 NY NY NY
Irene dau 8 NY NY NY
Harold son 6 NY NY NY


Saint Peter's Lutheran Cemetery
Town of Verona
Muth, Alice A. w/o Charles J. Muth Married Dec. 11, 1949 b 1932
Muth, Charles A. 1893 1984
Muth, Charles J. 1926
Muth, Ella M. w/o Fred P. Muth 1883 1954
Muth, Emma w/o Charles A. Muth 1901 1989
Muth, Fred J. 1908 1908
Muth, Fred P. 1883 1961
Muth, Harold F. 1913 1920
Muth, Jacob (father) 1854 1936
Muth, Rose (mother) 1861 1911
Muth, Shirley R. 1923 1923


http://oneida.nygenweb.net/ Oneida Co. Obituaries 1989
Deceased: Muth CHARLES A
DOD Jun 2'84
Father: Muth JACOB
Mother: KOCHESPERGER ROSINA
Spouse: VAN DE WALKER EMMA
Spouse DOD: 02/21/89
Survivors: 3

Deceased: Muth Emma
DOD: Feb 21'89
Father: VAN De WALKER Burton
Mother: Windlespecht Bertha
Spouse: Muth Charles A
Spouse DOD: 06/02/84
Survirors: 3

http://oneida.nygenweb.net/ Rome Sentinel Marriages 1904
Fred Muth md Minnie Mehrhof, Feb. 26, 1904