Hi, I found the following in Muhos, a neighbouring parish of Utajärvi:
An illegitimate child, Catharina, was born 14.10.1857, shortened Caisa/Kaisa. Her mother was maid Lisa Hämälä, from the farm Hämälä or Ketola in Laitasaari-village in Muhos. The mother was actually christened Johanna Elisabet, shortened Johanna Lisa.
The person you are searching for, Kaisa Johanna Lisasdotter Ketola (later Kaisa Hämälä), is probably this Catharina, daughter of Johanna Lisa, from Ketola.
Though, I have not found any record of an illegitimate son of Kaisa's in 1872!
She takes her first communion in 1874. She gets married 28.7.1878 to Jacob Påhlsson Holappa (later Jaakko Paavonpoika Holappa). In Muhos Children/Preconfirmation Records there are noted two daughters and two sons. In the later Communion Book there is a note that the family resides in America.
Catharina, b. 14.10.1857 (christ. 21.10.);
SSHY Muhos Birth Records 1856-1878, [22.jpg];
https://www.sukuhistoria.fi/sshy/sivut/ ... 73&pnum=22 .
(same page in Digihakemisto [19.jpg];
https://astia.narc.fi/uusiastia/viewer/ ... 1245183767 .)
Johanna Elisabet (Zachris's daughter), b. 11.8.1835 (christ. 13.8.);
SSHY Muhos Birth Records 1827-1844, [133.jpg];
https://www.sukuhistoria.fi/sshy/sivut/ ... 1&pnum=133 .
(same page in Digihakemisto [122.jpg];
https://astia.narc.fi/uusiastia/viewer/ ... 1245176086 .)
SSHY Muhos Communion Book 1854-1861,
- p. 238;
https://www.sukuhistoria.fi/sshy/sivut/ ... 0&pnum=135 .
(same page in Digihakemisto;
https://astia.narc.fi/uusiastia/viewer/ ... 1245111033 .)
SSHY Muhos CB 1862-1871 (-1881),
- p. 212;
https://www.sukuhistoria.fi/sshy/sivut/ ... 7&pnum=108 .
(same page in Digihakemisto;
https://astia.narc.fi/uusiastia/viewer/ ... 1245122692 .)
- p. 302;
https://www.sukuhistoria.fi/sshy/sivut/ ... 7&pnum=153 . (In the middle of the page with husband, at the bottom of the page with husband and two daughters.)
(same page in Digihakemisto;
https://astia.narc.fi/uusiastia/viewer/ ... 1245122692 .)
SSHY Muhos CB 1881-1890,
- p. 400;
https://www.sukuhistoria.fi/sshy/sivut/ ... 1&pnum=178 .
SSHY Muhos Marriage Records 1860-1883;
https://www.sukuhistoria.fi/sshy/sivut/ ... 2&pnum=120 .
SSHY Muhos Children/Preconfirmation Records 1881-1890; (left page, at the bottom, wrong surname according to birth records, should be Holappa!);
https://www.sukuhistoria.fi/sshy/sivut/ ... 3&pnum=149 .
I hope this is the right Kaisa and her family.
Birgit S.