As discussed in the entry for √AR, for a considerable time in Tolkien’s life the basis for the word “and” was the root √AR with the sense “beside”, so that Q. A ar B “A and B” originally had the sense “A beside B”. However, at some point during the writing of the Lord of the Rings he decided that the Sindarin word for “and” was a, making √AR no longer suitable for its etymology.
From this point forward Tolkien toyed with two possible roots for “beside; and”, either √AD and √AS, with another option √ÑAR considered and rejected in 1957 (PE17/169). It seems Tolkien vacillated between the √AD and √AS, so an exact timeline is hard to nail down. Their primary difference would be in the prevocalic form of Sindarin “and”: either edhil adh edain [ada > aða] or edhil ah edain [asa > aha] for “elves and men”. The most detailed breakdown of these two possibilities appeared in Tolkien’s notes on words in The Lord of the Rings, probably written in the late 1950s (PE17/41). In these notes he kept flipping back and forth between ancient asa and ada, though ultimately settling on ada.
However, ah appeared in the title of the document Athrabeth Finrod ah Andreth “The Debate of Finrod and Andreth” most likely written in 1959 (MR/329), and in a 1968 note Tolkien said the primitive form was as with S. ah “and” before vowels and a before consonants (VT43/30). So either Tolkien reversed himself again and adopted √AS, or he continued to vacillate. For purposes of Neo-Eldarin, I think it is best to assume the root was √AS.
One result of the change of √AR >> √AS/√AD is that the Sindarin prefix ar- could no longer mean “beside” as it did in Noldorin. Indeed, in notes on The Rivers and Beacon-hills of Gondor written in the late 1960s he said “Arnen originally was intended to mean ‘beside the water’, sc. Anduin, but ar- in this sense is Quenya, not Sindarin” (VT43/17). This leaves us with no good word for “beside” in Sindarin; at one point I coined a neologism sa for this purpose, but it is a real stretch.
As a final note, these 1950s and 1960s roots were not the first time Tolkien used √AS for something like “beside”. All the way back in the 1910s, Tolkien had the root √AS(A) in both the Quenya and Gnomish Lexicons (QL/33; GL/48) with derived forms like ᴱQ. ar “to, against, next, on (wall)” (QL/33), G. hath- “close to, by, beside, touching” (GL/48), and [maybe] G. art “beside, alongside of” (GL/20), though the last form may be unconnected given the unlikeliness of s > r in Gnomish.
The root √AR has a long and complex history in Tolkien’s writing. For many years, it was the basis for the word ar “and”. Its earliest precursor was the root ᴱ√ARA or ᴱ√ƷARA in the Qenya Lexicon variously glossed “spread, extend sideways” or “wide places” (QL/32). The Gnomish derivatives of this root such G. garw “sown field” (GL/38) vs. ᴱQ. arwa made it clear the true primitive form was √ƷARA (in Gnomish, ʒ- > g-). Some of the early derivatives of √ƷARA such as G. gar(th), ᴱQ. arda “place” were later transferred to the root ᴹ√GAR so they could retain this gar-/ar- distinction.
Of the derivations that remained under √AR, the most notable were ᴱQ. are “beside, along” and the conjunction ᴱQ. ar(a) “but” (QL/32). The latter changed in meaning to ar “and” by the end of the 1920s, for example in the Oilima Markirya poem. This carried into the 1930s paradigm for the root ᴹ√AR, as seen by its entry in The Etymologies with its derivatives ᴹQ. ara “outside, beside” (the basic sense of the root) and ᴹQ. ar “and” (Ety/AR²). The most common Noldorin word for “and” in this period was likewise ar (TAI/150; SD/128-129), and in prefixal form ar- “outside, beside” sometimes developed a privative sense “without”, most notably in arnediad (†arnoediad) “without reckoning, numberless” as in N. Nirnaith Arnediad “(Battle of) Unnumbered Tears” (Ety/AR², NOT) which in Sindarin became Nirnaeth Arnoediad.
In some etymological notes from the 1950s Tolkien retained the root form ara “alongside” (VT43/33), but there were already cracks forming in this system, forced by Tolkien’s decision that the Sindarin word for “and” was a rather than ar, a change that first appeared Lord of the Rings drafts from the 1940s (TI/182). By the late 1950s Tolkien was experimenting with new roots √AD(A) and √AS for the meaning “beside” and the derivation of Q. ar, S. a “and”; see those entries for later developments in this semantic space of “beside”.
As for the root √AR itself, it shifted in meaning to “beyond, further than” in Quenya Notes (QN) from 1957, becoming the basis for “royal” roots like √ARAN “king” or √ARAT “noble” (PE17/147). In this revised meaning, it might still be able to retain a “privative” sense in Sindarin words like †arnoediad “unnumbered” (perhaps = “✱beyond numbering”), though it is also possible Tolkien simply never revisited the etymology of this Sindarin word.