There is online a 1900 dissertation on Cybele and Attis by Grant Showerman, The great mother of the gods, Bulletin of the University of Wisconsin, vol. 1 (1898-1901). p. 219, online here, starting on p. 219, which is very good on ancient literary sources for its statements. Thanks to Christopher Ecclestone for the link! Some notes:
Herodian gives (book 1, ch. 11) an account of the origins of the cult of Cybele, although not mentioning Attis. Pliny the Elder also gives an explanation of the term ‘Gallus’ for the eunuch priests, in NH V.147, VI.4.
He says that the legend of Attis first appears “in the elegiac poet Hermesianax, around 340 BC” (p.240). No reference is given; but about a hundred lines of this otherwise lost writer is preserved by Athenaeus, xiii. 597. This can be found online here, and Hermesianax starts on p. 953. However it seems very questionable that any of this really refers to Attis; and a look at Vermaseren, Cybele and Attis, p.111 tells us that he means the statements of Pausanias, which the latter attributes to Hermesianax.
The thesis then lists the four different legends known to us (respectively in Pausanias, Arnobius the Elder, Diodorus Sicilus, Firmicus Maternus). Different accounts again appear in Ovid, Sallustius and Julian.
An identification of Attis with Adonis is given by Hippolytus, Refutation, V.9, and apparently Socrates HE III.23 refers. This is a description of the confused system of the Naassenes. But it tells us little except that the Naassenes were syncretists, or liberals as they prefer to be known today.
Attis is also referred to by Theocritus, XX.40 ff. About the same time, Neathes of Cyzicus wrote something about Attis which is referred by Harpocration the lexicographer as a myth, under ‘Atths’. Nicander at the start of the 2nd century BC mentions him in the context of the creation of galloi (Alex. 8).
There is clear evidence that Attis was not worshipped at Rome in Republican times; Dionysius of Halicarnassus says (II.19.2) ca. 30 BC that:
And no festival is observed among them as a day of mourning or by the wearing of black garments and the beating of breasts and the lamentations of women because of the disappearance of deities, such as the Greeks perform in commemorating the rape of Persephonê and the adventures of Dionysus and all the other things of like nature.
whereas such a procession did exist as part of the annual rites of Cybele, for Attis, in imperial times (p.263). A similar piece of information can be found in the Fasti praenestini (ca. 3 AD). (See article in TAPA 1900, p.46 f). At this date he was merely a mythological person associated with Cybele, rather than a separate deity.
In the calendar in the Chronography of 354, on March 22 “arbor intrat” — the sacred tree of Cybele is taken into the sanctuary. John the Lydian, De Mens. IV, 36, 41 f. gives information on the dates of the festivals. On March 24 is the “sanguem” in the calendar, labelled elsewhere as “dies sanguinem” (Treb. Poll. Claudius IV). This was the day when the galli got the chop.
The scholiast on Nicander’s Alex. 8 writes: τοποι ἱεροὶ ὑπογειοι ….. οπου ἐκτεμνόμενοι τὰ μήδεα κατετίθεντο οἱ τῷ αττει καὶ τῇ ῥέᾳ λατρεύοντες. indicating that in the taurobolium, the removal of the bull’s genitals commemorates Attis.
Attis is described by Michael Psellus as the “Phyrgian Zeus” (Peri Onomaton 109), and there is a reference in Arrian.