Dear Ms. McCoy,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located Supplemental Manifests of Alien Passengers and Crew Members Who Arrived on Vessels at New York, New York, Who Were Inspected for Admission, and Related Index, 1887-1952 in the Records of the Immigration and Naturalization Service (Record Group 85) and view the various lists for the years of interest.
We also searched Ancestry and located a possible entry for Rose and Shimeon on 2 pages with the information that was provided. They were held for a Board of Special Inquiry (the “admitted” stamp is over the letters “SI” and were found on a detainee list where they were noted as likely to become a public charge. (LPC). Although Shimeon was held for 4 days (you can see the meal numbers at the far right on the detainee list), they were both ultimately admitted to the US. On the passenger arrival record both have hand written notations indicating that later Certificates of Arrival were issued which would hint that they may have pursued US citizenship. It may be worthwhile for you to search for their Naturalization records from the appropriate NARA field site(s). There may be a fee for using Ancestry. Instead, you may view these records online at one NARA's facilities for free via a NARA PC. For the nearest NARA location, please consult our web page at https://www.archives.gov/locations/. Also, some of the images from Ancestry are available for free on Family Search at https://www.familysearch.org/en/.
If you have not already done so, we also suggest that you search the US Citizenship and Immigration Services (USCIS) Genealogy Program’s website to locate their records. USCIS maintains immigration and naturalization related files that its predecessor, Immigration and Naturalization Service (INS) created during the mid-1900s. You can submit an Index Search to determine if any records may exist. They may have a Certificate File (C-File) that will contain their Petition for Naturalization and/or Certificate of Naturalization in it.
We suggest that if you know the city and/or state location for where the naturalization occurred, then please search this web page www.archives.gov/research/court-records to identify the NARA facility and Federal court. NARA will have a copy of the original Petition for Naturalization that would have been submitted through a Federal court. We also suggest that you review Naturalization Records for additional research tips.
We hope this is helpful. Best of luck with your family research!
[Some Information provided by Elizabeth Burnes, Subject Matter Expert]