Following up on a previous answer:
For more information about alien registration forms, here are some resources that will show what kinds of information you can find in those records:
WWI Alien Registrations (these were created and held locally and do not survive for all areas; may be tricky to locate):
- An alien notion by Judy G. Russell, JD, CG, CGL, on The Legal Genealogist, posted Nov 16, 2012
- The forms of 1918: Hoosier-style by Judy G. Russell, JD, CG, CGL, on The Legal Genealogist, posted May 21, 2015 (this post introduced me to the database below)
- Genealogical Records of German Families of Allen County, Indiana, 1918 an online searchable database (based on the print publication) hosted by the Allen County Public Library. People had to list the names of their relatives on the forms, so there are references to family members living outside Allen County, Indiana. The post in the link above will show you an example of what information was extracted from the forms.
Try to find out where your people were living just before or during WWI and then look for an inventory of records for that area by using an inventory from the Works Progress Administration (WPA) Historical Records Survey. This guide by Bryan L. Mulcahy, Reference Librarian at Fort Myers - Lee County Library discusses the various kinds of records the WPA workers looked for and gives tips on how to locate the inventories.
WWII Alien Registrations:
- Aliens Among us by Judy G. Russell, JD, CG, CGL, on The Legal Genealogist, posted Feb 14, 2015, and the related webinar, Martha Benschura: Enemy Alien, available for purchase or by subscription at Legacy Family Tree Webinars
- Prologue Magazine, The A-Files: Finding Your Immigrant Ancestor by Elizabeth Burnes and Marisa Louie
- Online research guide at NARA: World War II Enemy Alien Control Program Overview
For an overview of immigration laws that will place these and other records in context, see Family Tree Magazine's research guide Timeline of US Immigration Laws.
The suggestion to look for the Alien Registration forms is a good one -- these record groups are especially valuable because they list the names and residences of other family members. If you get lucky, the forms might give you direct evidence of parents' names, and since they are rich in other identifiers, it can be easier than it is with other records to see whether the form belongs to your person or someone else with the same name.
With an arrival in 1906, it might be worthwhile to ask the USCIS Genealogy Program to do an index search to see if they have records for your great grandmother Emilie. When you apply, give them all known variants of her name. Their brochure has information about how to do a request and their website can give you an overview of the historical records that are available at USCIS.