Quenya does not have an indefinite article, but it does have a set of indefinite pronouns: mo “some (indefinite) person” and ma “some (indefinite) thing”:

mo, indefinite personal pronoun “somebody, one”.
ma, neuter personal pronoun “something, a thing”.

For the indefinite mo the inclusive 1.pl.= “we, you and I (and others associated)” was often used, espec. colloquially, like E. “you” (notes from the late 1960s, PE22/154).

The personal indefinite pronoun mo is often used as an indefinite subject in much the way that English sometimes uses the word “one”: alasaila ná lá kare tai mo nave mára “it is unwise not to do what one judges good” (VT42/34). This use of indefinite subjects sometimes serves a function similar to English passive voice (PE22/154 note #57), for example: mo quete i Eldar vanime nér “one says the Elves were beautiful” or in more colloquial English “it is said the Elves were beautiful”. A suffixal form -mo frequently functions as an agental suffix: onótimo “reckoner” (MR/49), more literally “count-up-person” as suggested by Carl Hostetter and Patrick Wynne (VT34/30).

We have fewer examples of how the neuter indefinite pronoun ma was used, and its use may be limited to objects, not subjects, such as: yé mána ma “what a good thing” (PE17/162). This is because the neuter indefinite pronoun is identical in form to the interrogative particle ma, and if it were to appear at the beginning of a sentence, the phrase would probably be mistaken as a question. There is no such confusion with personal interrogatives, because “who” was man, not mo. For example, “something must be done” might be mauya mo care ma = “it is needed that someone do something” in Quenya.

Origins of indefinite pronouns: The personal indefinite mo was derived from primitive ✶mō which simply meant “person” (VT47/35), while the neuter indefinite ma was probably related to and derived from the interrogative root √MA.

Conceptual Development: The Early Qenya Grammar (EQG) has an indefinite article in the form of the suffix ᴱQ. -(u)ma (PE14/42, 71), almost certainly the precursor to the indefinite/interrogative ma as suggested by Christopher Gilson (PE17/68). We don’t know what the indefinite pronouns were at this stage, however, and it seems that impersonal/indefinite subjects were simply omitted entirely in EQG:

Note the neuter is never used as an impersonal subject: there is no prefix used at all in that case, as: uqe “it rains”; tiqe “it thaws” (PE14/56).

In Quendian & Common Eldarin Verbal Structure from the 1940s, Tolkien said Quenya had an indefinite subject pronoun ᴹQ. a¹ (PE22/94), and this pronoun also appeared in the contemporaneous Quenya Verbal System, in constructions resembling passive voice: i·nér né raiqa ar sí aphasta “the man was angry but now is in good humor” where a-phasta = “it pleases (him)” (PE22/124); masse akime aldar “where are the trees” more literally “where does one find trees” (PE22/125).

These same 1940s documents had a generic personal definite pronoun ᴹQ. e. The pronoun e briefly reappeared in notes from the late 1960s as an indefinite personal pronoun, but was soon changed to mo (PE22/154 notes #57, 68). For the most part, in the 1950s and 60s Tolkien seem to use mo/ma for indefinite pronouns, as discussed above.

Neo-Quenya: The use of mo/ma as indefinite pronouns is not very controversial, and they are usually interpreted as “someone, something”. This begs the question of how to express the concept of “anyone, anything”. There is another later pronoun aiquen glossed “if anybody, whoever” (WJ/372) which is often used in Neo-Quenya writing for “anybody”. Likewise, Helge Fauskanger coined a neologism ᴺQ. aiqua for “anything” based on ilqua “everything”. Both of these words appear with these meanings in his Neo-Quenya New Testament (NQNT).

From these we can extrapolate ᴺQ. ailume “anytime” and ᴺQ. ainome “anyplace, anywhere”, following the pattern of silume, talume and sinome, tanome. These introduce a problem for “sometime, someplace”, which can’t be easily generalized from mo/ma. The best options I’ve seen to date are ᴺQ. nalume “sometime” and ᴺQ. nanome “someplace” based on námo “somebody”, as suggested by Lokyt in a discussion on the Aglardh forums in late 2019. But this is all very deeply speculative, and may easily be overturned by future publications.