ACL for a Single User

[NIRANJAN S2]

I am trying to restrict a Particular user to edit a field in CI table through ACL. The ACL is working fine while impersonating the user and checking it in the frontend, but the ACL is not restricting the user if a Schedule script is run on his behalf (i.e "Run as").
Any solutions to restrict a user in background(through schedule job or script) to change a field in the table ?

[Mike_R]

What kind of access does this user have? And why is a scheduled script running as this user's profile?

[NIRANJAN S2]

It is a Service Account and has Admin access, this service account is used to update records in the CI table using schedule jobs.