I'm assuming you mean a USCIS "AA" Certificate file for Jon, since he was born abroad to US citizen parents.
No, no file or record of his derivative citizenship would be created upon his arrival as an infant in ca. 1900/1901. Congress did not create the authority for any part of the government to issue such certificates/create such files until 1929, and gave that authority to the INS, now USCIS. Even then, the 1929 legislation required the derivative citizen (Jon) to be 21 years or older to apply.
What this means is that in or after 1929 Jon could apply for a AA Certificate of Derivative Citizenship. He was not required to do so, but the reason Congress created the authority was because people like him needed some proof of their citizenship. If he did so, there would be a file. If he applied and the certificate was issued between 1929 and March 31, 1956, it would be a AA Certificate File (C-file) with USCIS. If he applied and the certificate was issued on or after April 1, 1956, it would be in an A-File.