Erik Hämäläins were common in Leppävirta, Kuopio, e.g. one born in 1755 to an Erik

from Terhi Arpalahti...
There was a soldier Erik Modig, whose original name was Hämäläinen,
marr. 6.4.1744 Vsri Anna Johansdr. This couple had at least 7 child-
ren. There were twins Jakob and ANNA born 5.6.1774 Muurue, bapt.
12/6. This Anna MAY be your Anna Eriksdr Hämäläinen. This soldier
Erik Modig died 12.2.1779 Muurue (58y).

thus born 1721; from data below he had to be born before 1738. From HisKi, there is only one candidate:
1.12.1722 Keitelenpohja Broof. Erick Bengtss. Hämäläin Walborg Simonsd:r Erick

His father was likely a Henrik or Petter from HisKi births of other Modigs in the same place. From HisKi..

12.1.1765 Taimo Erick Modig Anna Johansd:r Henric
11.2.1767 Taimonemi Erick Modig Anna Johansd:r Petrus
5.6.1774 Murue Sold. Erick Modig Anna Johansd:r Anna (tv) and Jacob
and earlier..
1.12.1758 Kockila Erick Hämäläin. Anna Colemain Ericus
20.8.1761 Kockila Erick Hämäläin Anna Johansd:r Johannes

these are prob. 6 of the 7 children mentioned by Terhi A.

1799-1810 RK Viitasaari Wuorilax “svar mor, 1735” (crossed out)