Please share census record(s) where your Alta Harriett and Jess are in the same household(s)? I'd like to add "two cents" to this search but hesitate 'cause I cannot confirm your ancestor. Regardless, his original social security card application should include names of parents? You can obtain a copy http://www.socialsecurity.gov/online/ssa-711.pdf
This is your only posting under the current screen logon.