Hyginus reports details of the Poseidon myth. Fab., 3, 10, 12, 14, 17, 89, 140, 157, 166:


(Fab3): Phrixus
Phrixus and Helle were driven mad by Bacchus as they wandered in the woods; their mother Nebula is said to have come and brought a golden ram, the son of Neputune and Theophane. She commanded her children to climb upon its back and to travel to Colchis, to king Aeolus, the son of the Sun, and there to offer the ram as sacrifice to Mars.
The story is told that this happened. When they had climbed up and the ram had carried them over the sea, Helle fell off the ram — the sea there is called the Hellespont after this event. But the ram took Phrixus all the way to Colchis. There, according to his mother's instructions he sacrificed the ram and put its golden fleece in the temple of Mars. They say that Jason, the son of Aeson and Alcimedis sought the fleece while a serpent guarded it. 3) Aetes, however, freely received Phrixus and gave him his daughter Chalciope in marriage. She later bore him sons. But Aetes feared that they would usurp his realm, because he had discerned from prodigies that he should beware of death at the hands of Aeolus' offspring; and for this reason he murdered Phrixus. 4) His sons, however, Argus, Phrontis, Melas, and Cylindrus, embarked in a raft so as to cross to their grandfather Athamas. When Jason came seeking the fleece, he rescued them from their shipwreck on the island of Dia and returned them to their mother Chalciope, a kindness for which he was commended to their sister Medea.
(Fab10): Chloris
Chloris was the daughter of Niobe and of Amphion who survived from the seven daughters of Niobe. Neleus, son of Hippocoön, had her to wife and begat twelve sons from her. 2) When Hercules was razing Pylos, he murdered Neleus and ten of his sons. The eleventh, however, Periclymenus, escaped with the help of Neptune having been transformed into the appearance of an eagle. 3) For the twelfth son, Nestor, was at Troy, he who is said to have lived for three generations with Apollo's help. For, the years that Apollo reduced from Chloris' brothers' lives he transferred to Nestor's.
(Fab12): Pelias
An oracle decreed to Pelias, the son of Cretheus and Tyros, that he should sacrifice to Neptune, and if some "monocrepis" person, i.e. a person shod on only one foot, should come along, then his death would be nigh. 2) When he was offering the annual rites to Neptune, Jason, the son of Aeson (i.e. the son of Pelias' brother), intending to offer sacrifice, left his footwear behind while crossing the river Euhenus. He left it behind so that he could quickly get to the sacrifices. 3) Pelias perceived this and, mindful of the fates' decree, ordered him Jason to seek from his enemy Aetes the fleece of the ram which Phrixus sacrificed to Mars, the golden one that was at Colchis. 4) Jason mustered the generals of Greece and set out for Colchis.
(Fab14): The Mustered Argonauts
Jason was the son of Aeson and Alcimede, who was daughter of Clymenus, and general of the Thessalians. Orpheus, son of Aeagrus and of the Muse Callipe, was a Thracian, from the city of Flevia which is on Mt Olympus near the river Enipeus, and also an inspired citharist. Asterion, from the city of Pellene, was the son of Pyremus ... Caeneus, son of Elatus from Magnesia, showed that Centaurs cannot wound themselves with the sword, but rather with tree trunks shaped into wedges. Many authors say that this Caeneus was once a girl; Neptune raped her but granted her request to be turned into a boy and made invunerable. But, this never happened, nor can it ever happen that a human being be made invulnerable by a sword or turned from a woman into a man. 5) Mopsus the son of Ampycus and ...
(Fab 17): Amycus
Amycus was the son of Neptune and Melia and king of Bebrycia. He used to compell those who entered his kingdom to box with him and he destroyed those who lost. When the Argonauts came and he challenged them to box, Pollux fought against him and killed him.
(Fab 89): Laomedon
Neptune and Apollo are said to have girt Troy with a wall. Laomedon the king vowed to them that he would sacrifice the firstlings born in his realm that year. Yet, he neglected this vow through greed. Some say that he had promised gold. 2) Because of his negligence Neptume send a sea-monster to trouble Troy; and for this reason the king sent an embassy to consult Apollo. Apollo responded in anger that if the daughters of Trojans were bound for the sea-monster the famine would end. 3) When many girls had been eaten and Hesione's number came up, she was chained to the cliffs. As Hercules and Telamon were sailing as Argonauts to Colchis they came to Troy and killed the sea-monster. They returned Hesione to her father swearing that when returned they would take her away to their own kingdom, and they also gave back the horses that walked on both water and on fields. 4) This pact also Laomedon broke, for he did not wish to return Hesione. Therefore, Hercules came to them on a mustered fleet to sack Troy; he killed Laomedon and bestowed the kingdom upon Podarces, Laomedon's infant son. Later he was called Priam from the Greek verb "to be purchased" ἀπὸ τοῦ πρίασθαι. 5) Hesione was rescued by Heracles and given in marriage to Telamon, and she bore him a son named Teucer.
    —— Translation by Roger Macfarlane


3. phrixvs. Phrixus et Helle insania a Libero obiecta cum in silua errarent, Nebula mater eo dicitur uenisse et arietem inauratum adduxisse,Neptuni et Theophanes filium, eumque natos suos ascendere iussit et Colchos ad regem Aeolum Solis filium transire ibique arietem Marti immolare. 2) ita dicitur esse factum; quo cum ascendissent et aries eos in pelagus detulisset, Helle de ariete decidit, ex quo Hellespontum pelagus est appellatum, Phrixum autem Colchos detulit; ibi matris praeceptis arietem immolauit pellemque eius inauratam in templo Martis posuit, quam seruante dracone Iason Aesonis et Alcimedis filius dicitur petisse. 3) Phrixum autem Aeeta libens recepit filiamque Chalciopen dedit ei uxorem; quae postea liberos ex eo procreauit. sed ueritus est Aeeta ne se regno eicerent, quod ei responsum fuit ex prodigiis ab aduena Aeoli filio mortem caueret; itaque Phrixum interfecit. 4) at filii eius, Argus Phrontis Melas Cylindrus, in ratem conscenderunt, ut ad auum Athamentem transirent: hos Iason cum pellem peteret, naufragos ex insula Dia sustulit et ad Chalciopen matrem reportauit, cuius beneficio ad sororem Medeam est commendatus.

10. Chloris Chloris Niobes et Amphionis filia quae ex septem superauerat. hanc habuit in coniugem Neleus Hippocoontis filius, ex qua procreauit liberos masculos duodecim. Hercules cum Pylum expugnaret, Neleum interfecit et filios eius decem, undecimus autem Periclymenus beneficio Neptuni aui in aquilae effigiem conuersus mortem effugit. nam duodecimus Nestor in Ilio erat, qui tria saecula uixisse dicitur beneficio Apollinis; nam quos annos Chloridis [et] fratrum Apollo eripuerat, Nestori concessit.
12. Pelias
Peliae Crethei et Tyrus filio responsum erat ut Neptuno sacrum faceret, et si quis monocrepis, id est uno pede calciatus superuenisset, tum mortem eius appropinquare. is cum annua sacra faceret Neptuno, Iason Aesonis filius, fratris Peliae, cupidus sacra faciendi, dum flumen Euhenum transiret calciamentum reliquit; quod ut celeriter ad sacra ueniret neglexit. id Pelias inspiciens, memor sortium praecepti iussit eum pellem arietis quam Phrixus Marti sacrauerat inauratam Colchis ab rege Aeeta hoste petere. qui conuocatis Graeciae ducibus Colchos est profectus.
14. Argonautae Convocati
Iason Aesonis filius et Alcimedes Clymeni filiae et Thessalorum dux. Orpheus Oeagri et Calliopes Musae filius, Thrax, urbe Fleuia, quae est in Olympo monte ad flumen Enipeum, mantis citharista. Asterion Pyremi filius, ... 4) hic Caeneus Elati filius, Magnesius, ostendit nullo modo Centauros ferro se posse uulnerare, sed truncis arborum in cuneum adactis; hunc nonnulli feminam fuisse dicunt, cui petenti Neptunum propter conubium optatum dedisse ut in iuuenilem speciem conuersus nullo ictu interfici posset. quod est nunquam factum, nec fieri potest ut quisquam mortalis non posset ferro necari aut ex muliere in uirum conuerti. Mopsus Ampyci et Chloridis filius...
17. Amycus
Amycus Neptuni et Melies filius, Bebryciae rex. in huius regna qui uenerat caestis cogebat secum contendere et deuictos perdebat. hic cum Argonautas prouocasset ad caestus, Pollux cum eo contendit et eum interfecit.
89. Laomedon
Neptunus et Apollo dicuntur Troiam muro cinxisse; his rex Laomedon uouit quod regno suo pecoris eo anno natum esset immolaturum. id uotum auaritia fefellit. alii dicunt aurum eum promisisse. 2) ob eam rem Neptunus cetum misit qui Troiam uexaret; ob quam causam rex ad Apollinem misit consultum. Apollo iratus ita respondit, si Troianorum uirgines ceto religatae fuissent finem pestilentiae futuram. 3) cum complures consumptae essent et Hesionae sors exisset et petris religata esset, Hercules et Telamon cum Colchos Argonautae irent eodem uenerunt et cetum interfecerunt, Hesionenque patri pactis legibus reddunt, ut cum inde rediissent secum in patriam eam abducerent, et equos qui super aquas et aristas ambulabant. 4) quod et ipsum Laomedon fraudauit neque Hesionen reddere uoluit; itaque Hercules ad eos nauibus comparatis ut Troiam expugnaret uenit et Laomedontem necauit et Podarci filio eius infanti regnum dedit, qui postea Priamus est appellatus ἀπὸ τοῦ πρίασθαι. 5) Hesionen recuperatam Telamoni concessit in coniugium, ex qua natus est Teucer.
140. Python
Python Terrae filius draco ingens. hic ante Apollinem ex oraculo in monte Parnasso responsa dare solitus erat. huic ex Latonae partu interitus erat fato futurus. 2) eo tempore Iouis cum Latona Poli filia concubuit; hoc cum Iuno resciit, facit ut Latona ibi pareret quo sol non accederet. Python ubi sensit Latonam ex Ioue grauidam esse, persequi coepit ut eam interficeret. at Latonam 3.1 Iouis iussu uentus Aquilo sublatam ad Neptunum pertulit; ille eam tutatus est, sed ne rescinderet Iunonis factum, in insulam eam Ortygiam detulit, quam insulam fluctibus cooperuit. quod cum Python eam non inuenisset, Parnassum redit. 5 at Neptunus insu- 4.1 lam Ortygiam in superiorem partem rettulit, quae postea insula Delos est appellata. ibi Latona oleam tenens parit Apollinem et Dianam, quibus Vulcanus sagittas dedit donum. post diem quar- 5.1 tum quam essent nati, Apollo matris poenas exsecutus est: nam Parnassum uenit et Pythonem sagittis interfecit (inde Pythius est dictus), ossaque eius in cortinam coniecit et in templo suo posuit, ludosque funebres ei fecit, qui ludi Pythia dicuntur.
157. Neptuni Filii neptvni filii. Bootus et Hellen ex Antiopa Aeoli filia. Agenor et Belerophon ex Eurynome Nysi filia. Leu- conoe ex Themisto Hpsei filia. ri ex Alcyone Atlantis filia. Abas ex Aretusa er filia. [†Ephoceus ex Alcyone Atlantis 2.1 filia]. [Belus]. Actor . . . . . . Dcts ex Agamede Aug filia. Euadne ex †Lena Leucippi filia. Megareus ex Oenope Epopei filia. Cygnus ex Calyce Hecatonis filia.

ericlmenus et Aeus ex 3.1 Astyle Phoenicis filia. Neleus et Pelias ex Tyro Salmonei filia. Euphemus et Lycus et Nyctus ex Celaeno †Ergei filia. Peleus 4.1 †Arprites. Anaeus . . . . . . . mopus ex Chiona Aquilonis filia . . . . . . . Ammone . . . . item Cyclops phemus . . . . †Metus et Melite Busiris filia.
166. Erichthonius erichthonivs. Vulcanus Ioui ceterisque diis †soleas aureas† ex adamante cum 166.1.1 fecisset, Iuno cum sedisset, subito in aere pendere coepit. quod cum ad Vulcanum missum esset ut matrem quam ligauerat solueret, iratus quod de caelo praecipitatus erat negat se matrem ullam habere. 5 quem cum Liber pater ebrium in concilio deorum addu- 2.1 xisset, pietati negare non potuit; tum optionem a Ioue accepit, si quid ab iis petiisset impetraret. tunc ergo Neptunus, quod Miner- 3.1 uae erat infestus, instigauit Vulcanum Mineruam petere in coniu- gium. qua re impetrata in thalamum cum uenisset, Minerua monitu Iouis uirginitatem suam armis defendit, interque luctandum ex semine eius quod in terram decidit natus est puer qui inferiorem 5 partem draconis habuit; quem Erichthonium ideo nominauerunt 4.1 quod ἔρις Graece certatio dicitur, χθὼν autem terra dicitur. quem Minerua cum clam nutriret, dedit in cistula seruandum Aglauro Pandroso et Herse Cecropis filiabus. hae cum cistulam aperuis- 5.1 sent, cornix indicauit, illae a Minerua insania obiecta ipsae se in mare praecipitauerunt.