- In 1870 she is Fredericka.
In the 1880 census, there are 46 Mosers living in Erie County. She is maybe Juliana. It may be because 1) she has a son named Christian; 2) she has a son named Charles in both census (though he's aged 9 in 1870 and 14 in 1880); 3) she is a widow in 1880. That's thin evidence. Note the number of children who don't appear, then, in 1870:
in 1870, her children are: Frederick (12), Fredericka (11), Anne (11); Charles (9), and Samuel (6).
In 1880, the children are: Christian (26), John (24), Katherine (19), Joseph (17); Charles (14), Henry (12), Caroline (10). In the 1880 census as well her family's birth places also differ from 1870, in that the oldest three are born in Baden. If this is the same family, that would give an estimate of when this family immigrated. The three oldest (aged 26, 24, 19) were born in Baden; the next, aged 17, was born in New York. This would place immigration around 1861-63.