This question is complicated by a slight vagueness in how the OP expresses it, which immediately brings in extra languages.
The "point" was simple in the original and KJV.
The original text is Greek: ἰῶτα ἓν ἢ μία κεραία
Don't add one letter i or one 'keraia' which is a peculiar diacritic which can be read about and examples seen at: https://en.wikipedia.org/wiki/Greek_numerals#Description
An iota is a single mark with the writing implement - which could be pen, chisel or stylus. ι - it often has a breathing mark ἱ or accent ί but what's being talked about is the 1-stroke core of the letter.
Keraias might look like something we don't need anymore: they're a reading-aid to help distinguish letters from letters-used-as-numerals, especially within the big blocks of capital-letter text that used to fill the whole page.
We do have something similar in these internet days - some fonts use a cross-stroke to distinguish an O from a 0. Physical letterplate printing also had them on 7s to avoid them being mistaken for a capital-L, which survives in some computer fonts even though there's no longer a risk of the 7 being inserted upside-down.
What KJV mean by "jot" and "tittle" is potentially harder to work out - "jot" is derived directly from "iota" and we still have "jot it down" as in to mark the page with the pen, but "tittle" really only has survived as the KJV's gloss for 'keraia'. From wikipedia it seems it firstly referred to the marks that completed a letter: such as the dot on an i. https://en.wikipedia.org/wiki/Tittle
Which makes KJV's translation nattier than the original, describing a single letter by its parts.
To be nattier than is not to add an iota though, so that's okay.
The KJV famously liked Ancient Hebrew above Greek in their approach to the Old Testament, but there's no obvious reason to think they are bringing in a different Hebrew letter by saying "jot or tittle".
Meyer discusses this though, and the idea seems to have been of interest in ancient time.
Plut. Mor. p. 1100 A, 1011 D), especially also in single letters (Origen, ad Psalms 33), by which, for example, the following letters are distinguished, כ and ב, ר and ד, ה and ח.
The Origen reference in the Psalms should be in here somewhere: https://books.google.co.uk/books?id=sLpDsFbzv2wC&redir_esc=y but I'm not masochistic enough to wade into a big pdf of Migne's edition without an express request from the OP.
That deeper analysis doesn't seem necessary - it's nice that Greek, Hebrew and English can for once avoid a translation difficulty - thanks to our shared admiration of the Phoenician letter "yodh" (י).