I think John is correct and believe the F N hst at 9 & 3 is the earliest headstamp used on FN autopistol cartridges. This is the headstamp on some of a batch of 7.65mm Browning dummies that were found a few years ago in a Liege Museum and were probably from the early development of the Browning M1899 pistol (predecessor to the more common M1900). There were also unheadstamped rounds.
It seems probable that these are the very early dummies since they occur with both rimless and semi-rimmed cases. The first 7.65x17mm cases made for John Browning by Winchester in Feb 1898 were rimless cases and were likely for the prototype of the M1899 pistol which, in 1897, went to Belgium with FN representative Hart Berg. This pistol was probably returned to John Browning during a visit in Jan 1898 and Browning had Winchester make some cartridges in 7.62x17mm rimless at that time so he could shoot his pistol. These would have been the first 7.65x17mm autopistol cartridges produced in the US.
So the FN headstamp could have been as early 1899 or so.
FN was producing 9x19mm as early as 1921 (from a specimen in my collection). These early FN headstamps have serifs. No 9x19mm has shown up with just the F N, the earliest 9x19mm FN commercial headstamps are F N *. The serifs occur on dated rounds through 1927 but are not on F N 36 cartridges so the serifs were dropped sometime between 1927 and 1936 on 9x19mm dated rounds and probably on the F N * commercial rounds and on other FN commercial autopistols rounds including 6.35mmB. Since the later commercial FN rounds with serifs had the FN * headstamp, my personal guess is that the FN headstamp used on your 6.35mm cartridge was dropped sometime in the mid-1920 or earlier.
My guess is that your cartridge was produced sometime before the mid-1920.
Lots of supposition in the above, but without records, ideally dated drawings, that is all we have.
If anyone has dated autopistol drawings showning the headstamp from the 1930s or earlier-PLEASE POST THEM!