[1] Aristophanes, Clouds 339. The phrase includes the Doric genitive plural of ke/stra. The word ke/stra is also glossed in Hesychius kappa2382: "a defensive weapon; a hammer; and a kind of fish". Photius, Lexicon kappa626 Theodoridis glosses it as mu/raina, "murry" (accusatives). The full headword phrase is also cited (in Attic) in tau 295.
[2] From the scholia vetera to the passage cited. The scholiast attempts a distinction between ke/stra [~ kestre/a] and kestreu/s. (On kestre/a see kappa 1430.) Both fish names derive from the literal meaning of ke/stra, "hammer". In LSJ, ke/stra is a sfu/raina (also a "hammer" fish, as identified by Athenaeus, Deipnosphists 7.323A-C = 7.122 Kaibel), and a sfu/raina is either a "bicuda" ("Sphyraena spet") -- or a ke/stra. Dalby 2003 s.v. barracuda identifies the ke/stra and the sfu/raina with the Sphyraena sphyraena, the European barracuda, called spet in French. The kestreu/s on the other hand is defined in LSJ as a mullet, and the ke/falos a kind of mullet. So LSJ is non-committal on the identity of the ke/stra and the kestreu/s. On the kestreu/s see also kappa 1432; on the identification with the ke/falos see kappa 1431.
[3] This gloss appears unique to the Suda.
[4] Mangling of a prescription in Phrynichus, Praeparatio Sophistica 12: "one will not correctly say te/maxos "slice" of meat, cake, or bread, but to/mos; te/maxos is said only of fish". By the time the phrase ends up in the scholia vetera on Aristophanes, Clouds 339b, it is rearranged: "te/maxos is said of fish and cake; never of meat". Though the Suda takes up the scholiast's prescription, "meat" is here substituted with "wheat", and in tau 295 with "peas".
[5] The "fasting mullet" (nh=stis kestreu/s), a commonplace of comedy (kappa 1432), is expanded out to the sentence given, "the mullet fasts", in Athenaeus, Deipnosophists 7.307C [7.79 Kaibel]; [Plutarch], Proverbs used by the Alexandrians 1.8; Pausanias, *)attikw=n o)noma/twn sunagwgh/ kappa29; Libanius, Letters 332.2; Gregorius, Proverbs 2.90; Apostolius 9.76. In LSJ s.v. kestreu/s, it is glossed as "of those too honest to make gains". The proverb is interpreted differently in Diogenianus 5.53 (Mazarin codex): "concerning the greedy, who pretend to fast; for the animal is insatiable" (on the gluttony of mullets, discussed in Aristotle, see kappa 1432). The two interpretations are merged together in Diogenianus 3.1 (Vienna codex) and Zenobius 4.52; in Diogenianus' wording: "concerning the very greedy. [Zenobius adds: For the mullet is so insatiable, that as a result those who gape and drink were called mullets, being greedy.] But it is also said concerning those who act honestly, but walk away with nothing more than justice. For while other fish eat each other, the mullet alone abstains from eating flesh, and feeds on mud". The Suda's wording combines Pausanias for the first sentence, and Diogenianus for the second. The proverbial saying is also glossed in Photius, Lexicon kappa624 Theodoridis (s.v. kestrei=s), whose wording overlaps with the Suda's.
[6] Namely "not carnivorous", as Diogenianus, Zenobius, and Athenaeus already indicate; see kappa 1432.