Speaking of Byzantion, a couple interesting inscriptions have been found dating from the period of Emperor Hadrian. The first (IByzantion 37) reads:

When Hadrian Caesar was official of the sacred (i.e. eponymous official of Byzantion) for the first time, the members of the society (thiasitai) dedicated this to Dionysos Parabolos on behalf of the gymnasium-director, Potamon Menodotos, an honor on account of his benefaction.  This was done when Menios son of Alexandros was priest (hiereus), Timogenes son of Timogenes was treasurer (tamias), Menodotos son of Timogenes was leader (prostatēs; or: patron), Chrysion son of Menios was benefactor, and Potamon son of Potamon was secretary (grammateus).

This was inscribed on a slab, which contained a relief described by Philip Harland in Associations of the Greco-Roman World in the following manner:

The relief depicts Dionysos on the right holding a wand (thyrsos) in one hand and a jug in the other, pouring out something into a container held by a boy on the left over a burning altar with a panther beside the altar. 

Παραβόλως is an otherwise unattested epithet for Dionysos, although in another inscription (IByzantion 38) we find:

When Hadrian Caesar was official of the sacred (i.e. eponymous official of Byzantion) for the second time, decree (?) of the Dionysoboleitans (Dionysoboleitai): Volusia Claudiane, wife . . . . (remainder missing).

Two proposals have been suggested. First that this form of Dionysos was somehow associated with Lake Parabolos or that the thiasos (or thiasoi if they are referring to separate groups) consisted of fishermen dedicated to Dionysos, as the Greek term bolos was used in reference to casting a net. 

This would certainly be unique since most of the time when fish come up in a Dionysiac setting it’s as part of a list of prohibited foods. For instance,  fish were forbidden to those being initiated into the mysteries at Eleusis, in which Dionysos had a part:

In the Eleusinian mysteries, likewise, the initiated are ordered to abstain from domestic birds, from fishes and beans, pomegranates and apples, which fruits are as equally defiling to the touch, as a woman recently delivered, and a dead body But whoever is acquainted with the nature of divinely-luminous appearances knows also on what account it is requisite to abstain from all birds, and especially for him who hastens to be liberated from terrestrial concerns, and to be established with the celestial Gods. (Porphyry, On Abstinence From Animal Food 4.16)

In a fragment of the Commentaries preserved in Athenaios Hegesander relates a curious tradition among the natives of Apollonia in Chalkis linking fish and the Anthesteria festival:

Around Apollonia of Chalkidike there flow two rivers, the Ammites and the Olynthiacus and both fall into the lake Bolbe. And on the river Olynthiacus stands a monument of Olynthus, son of Herakles and Bolbe. And the natives say that in the months of Elaphebolion and Anthesterion the river rises because Bolbe sends the fish apopyris to Olynthus, and at that season an immense shoal of fish passes from the lake to the river Olynthus. The river is a shallow one, scarcely overpassing the ankles, but nevertheless so great a shoal of the fish arrives that the inhabitants round about can all of them lay up sufficient store of salt fish for their needs. And it is a wonderful fact that they never pass by the monument of Olynthus. They say that formerly the people of Apollonia used to perform the accustomed rites to the dead in the month of Elaphebolion, but now they do them in Anthesterion, and that on this account the fish come up in those months only in which they are wont to do honour to the dead.

And fish were forbidden within Pythagoreanism:

Above all, Pythagoras forbade as food red mullet and blacktail, and he enjoined abstinence from the hearts of animals and from beans, and sometimes, according to Aristotle, even from paunch and gurnard. (Diogenes Laertios, Lives of Eminent Philosophers 8.19)

A tradition that overlapped considerably with Bacchic Orphism, as Herodotos notes:

The Egyptians wear linen tunics with fringes hanging about the legs, called ‘calasiris’ and loose white woolen mantles over these. But nothing of wool is brought into the temples, or buried with them; that is forbidden. In this they follow the same rules as the ritual called Orphic and Bacchic, but which is in truth Egyptian and Pythagorean; for neither may those initiated into these rites be buried in woolen wrappings. There is a sacred legend about this. (The Histories 2.81)

However the net is more promising, and one wonders if there is Orphic influence at work here. After all weaving and nets are a prominent feature of Orphism. Orpheus, according to the Suidas, authored a book entitled Diktyon or ‘The Net’ which likely discussed the generative weaving of Persephone. Indeed, Aristotle in his treatise On the Generation of Animals writes:

In the verse ascribed to Orpheus the various organs – heart, lungs, liver, eyes, etc. – were formed successively, for he says that animals come into being in the same way as a net is woven. (734a)

A more detailed and quite lovely account is given by Porphyry:

Let the stony bowls, then, and the amphorae be symbols of the aquatic Nymphs. For these are, indeed, the symbols of Dionysos, but their composition is fictile, i.e., consists of baked earth, and these are friendly to the vine, the gift of God; since the fruit of the vine is brought to a proper maturity by the celestial fire of the sun. But the stony bowls and amphorae are in the most eminent degree adapted to the Nymphs who preside over the water that flows from rocks. And to souls that descend into generation and are occupied in corporeal energies, what symbol can be more appropriate than those instruments pertaining to weaving? Hence, also, the poet ventures to say, “that on these, the Nymphs weave purple webs, admirable to the view.” For the formation of the flesh is on and about the bones, which in the bodies of animals resemble stones. Hence these instruments of weaving consist of stone, and not of any other matter. But the purple webs will evidently be the flesh which is woven from the blood. For purple woollen garments are tinged from blood and wool is dyed from animal juice. The generation of flesh, also, is through and from blood. Add, too, that the body is a garment with which the soul is invested, a thing wonderful to the sight, whether this refers to the composition of the soul, or contributes to the colligation of the soul (to the whole of a visible essence). Thus, also, Persephone, who is the inspective guardian of everything produced from seed, is represented by Orpheus as weaving a web and the heavens are called by the ancients a veil, in consequence of being, as it were, the vestment of the celestial Gods. (On the Cave of the Nymphs 6)

Her son Dionysos (whom Nonnos calls Zagreus) inherited his mother’s skill in weaving:

In him there had been resistless might, and a fierceness of disposition beyond control, a lust made furious, and derived from both sexes. He violently plundered and laid waste; he scattered destruction wherever the ferocity of his disposition had led him; he regarded not Gods nor men, nor did he think anything more powerful than himself; he contemned earth, heaven, and the stars. Now, when it had been often considered in the councils of the Gods, by what means it might be possible either to weaken or to curb his audacity, Liber, the rest hanging back, takes upon himself this task. With the strongest wine he drugs a spring much resorted to by Acdestis where he had been wont to assuage the heat and burning thirst roused in him by sport and hunting. Hither runs Acdestis to drink when he felt the need; he gulps down the draught too greedily into his gaping veins. Overcome by what he is quite unaccustomed to, he is in consequence sent fast asleep. Liber is near the snare which he had set; over his foot he throws one end of a halter formed of hairs, woven together very skilfully; with the other end he lays hold of his privy members. When the fumes of the wine passed off, Acdestis starts up furiously, and his foot dragging the noose, by his own strength he robs himself of his sex; with the tearing asunder of these parts there is an immense flow of blood; both are carried off and swallowed up by the earth; from them there suddenly springs up, covered with fruit, a pomegranate tree. (Arnobius of Sicca, Against the Heathen 5.5-6)

Zagreus in Crete had a special relationship with the net, which he used to capture animals and then set them free according to Carl Kerényi. Indeed while most derive this allonym of Dionysos from za agrios “the Great Hunter” as, for instance, the Etymologicum Gudianum does:

The one who greatly hunts, as the writer of the Alcmeonis said Mistress Earth, and Zagreus highest of all the Gods. That is, Dionysos. (s.v. Zagreus)

Hesychios proposed that it came from zagre, a “pit for the capture of live animals.” with nets being used to retrieve them.

This naturally reminds one of a certain Cretan Nymph:

Britomartis was born at Kaino in Crete of Zeus and Karme, the daughter of Euboulos who was the son of Demeter; she invented the nets which are used in hunting, whence she has been called Diktynna, and she passed her time in the company of Artemis, this being the reason why some men think Diktynna and Artemis are one and the same Goddess; and the Cretans have instituted sacrifices and built temples in honor of this Goddess. But those men who tell the tale that she has been named Diktynna because she fled into some fishermen’s nets when she was pursued by Minos, who would have ravished her, have missed the truth; for its is not a probable story that the Goddess should ever have got into so helpless a state that she would have required the aid that men can give, being as she is the daughter of the greatest one of the Gods. (Diodoros Sikeliotes, Library of History 5.76.3)

While Diodoros credits Euboulos’ daughter with the invention of nets, in Pliny that honor goes to Arachne:

The use of the spindle in the manufacture of woolen was invented by Closter son of Arachne, linen and nets by Arachne. (Natural History 7.196)

Incidentally, this is why the eighth month on our calendar (roughly August/September) is called Diktya (Δίκτυα) = the Net, and why we count this among the Sacred Weapons of our God.