Two different figures named Erginos seem to appear in Greek mythographic and poetic traditions. One is Erginos the son of Klumenos, a descendent of Minyas and king of Orchomenos. Another is a son of Apollo who traveled from Miletus to join the voyage of the Argonauts. Pindar appears to combine the two.

The son of Poseidon who appears in Argonautic tales is said to be from Miletus:
Apollonius Rhodes, Argonautica 186-189:

“And two other children of Poseidon arrived,
One abandoned the city of glorious Miletus,
Erginos,the other, overwhelming Angkaios,
Left the seat of Imbrasian Hera, Parthenia.
Both boasted of their knowledge of seafaring and war.”

καὶ δ’ ἄλλω δύο παῖδε Ποσειδάωνος ἵκοντο,
ἤτοι ὁ μὲν πτολίεθρον ἀγαυοῦ Μιλήτοιο
νοσφισθεὶς ᾿Εργῖνος, ὁ δ’ ᾿Ιμβρασίης ἕδος ῞Ηρης
Παρθενίην ᾿Αγκαῖος ὑπέρβιος· ἴστορε δ’ ἄμφω
ἠμὲν ναυτιλίης ἠδ’ ἄρεος εὐχετόωντο.

Orphic Argonautica, 152-4:

“Erginos also came, leaving begin the rich-grained field
Of Brankhos and the land of dusky Milêtos,
where the rivers of the much-wandering Maiander flow.”

῎Ηλυθε δ’ ᾿Εργῖνος, Βράγχου πολύπυρον ἄρουραν
ἐκπρολιπὼν καὶ τύρσιν ἐρυμνῆς Μιλήτοιο,
ἔνθα ῥοαὶ κλύζουσι πολυπλανέος Μαιάνδρου.

The other Erginos is a son of Klumenos and descendant of Minyas. He is from the city of Orkhomenos in Boeotia. Here is Apollodorus’ Story of Erginos (2.68-71)

“When Herakles arrived from the hunt, heralds arrived sent by Erginos so that they might seek reparations from the Thebans. The Thebans sent tribute for this reason: Menoikeos’ charioteer, named Periêrês, struck Klumenos the king of the Minyans with a stone and wounded him in the precinct of Poseidon at Ongkhêstos. When he was brought back to Orkhomenos half-dead he ordered his son Erginos to avenge his death as he died. Erginos attacked Thebes and forced them to make a treaty after killing many of them: they would send tribute to him for twenty years, a hundred bulls a year. Herakles tortured those heralds when he came upon them as they traveled to Thebes for the tribute. He cut off their ears and noses and hands and bound them by cords around their necks.

He told them to take this back as tribute for Erginos and the Minyans. Enraged over these things, Erginos led another army against Thebes. But Herakles took weapons from the Athenians, led the battle, killed Erginos, routed the Minyans and forced them to pay double the tribute to Thebes. During the battle, Amphitryon died while fighting nobly. For his excellence, Herakles received Kreon’s oldest daughter Megara and she gave him three children: Thêrimakhos, Kreontiadês, and Dêikoôn.”

ἀνακάμπτοντι δὲ αὐτῷ ἀπὸ τῆς θήρας συνήντησαν κήρυκες παρὰ ᾿Εργίνου πεμφθέντες, ἵνα παρὰ Θηβαίων τὸν δασμὸν λάβωσιν. ἐτέλουν δὲ Θηβαῖοι τὸν δασμὸν ᾿Εργίνῳ δι’ αἰτίαν τήνδε. Κλύμενον τὸν Μινυῶν βασιλέα λίθῳ βαλὼν Μενοικέως ἡνίοχος, ὄνομα Περιήρης, ἐν ᾿Ογχηστῷ Ποσειδῶνος τεμένει τιτρώσκει· ὁ δὲ κομισθεὶς εἰς ᾿Ορχομενὸν ἡμιθνὴς ἐπισκήπτει τελευτῶν ᾿Εργίνῳ τῷ παιδὶ ἐκδικῆσαι τὸν θάνατον αὐτοῦ. στρατευσάμενος δὲ ᾿Εργῖνος ἐπὶ Θήβας, κτείνας οὐκ ὀλίγους ἐσπείσατο μεθ’ ὅρκων, ὅπως πέμπωσιν αὐτῷ Θηβαῖοι δασμὸν ἐπὶ εἴκοσιν ἔτη, κατὰ ἔτος ἑκατὸν βόας. ἐπὶ τοῦτον τὸν δασμὸν εἰς Θήβας τοὺς κήρυκας ἀπιόντας συντυχὼν ῾Ηρακλῆς ἐλωβήσατο· ἀποτεμὼν γὰρ αὐτῶν τὰ ὦτα καὶ τὰς ῥῖνας, καὶ διὰ σχοινίων τὰς χεῖρας δήσας ἐκ τῶν τραχήλων, ἔφη τοῦτον ᾿Εργίνῳ καὶ Μινύαις δασμὸν κομίζειν. ἐφ’ οἷς ἀγανακτῶν ἐστράτευσεν ἐπὶ Θήβας. ῾Ηρακλῆς δὲ λαβὼν ὅπλα παρ’ ᾿Αθηνᾶς καὶ πολεμαρχῶν ᾿Εργῖνον μὲν ἔκτεινε, τοὺς δὲ Μινύας ἐτρέψατο καὶ τὸν δασμὸν διπλοῦν ἠνάγκασε Θηβαίοις φέρειν. συνέβη δὲ κατὰ τὴν μάχην ᾿Αμφιτρύωνα γενναίως μαχόμενον τελευτῆσαι. λαμβάνει δὲ ῾Ηρακλῆς παρὰ Κρέοντος ἀριστεῖον τὴν πρεσβυτάτην θυγατέρα Μεγάραν, ἐξ ἧς αὐτῷ παῖδες ἐγένοντο τρεῖς, Θηρίμαχος Κρεοντιάδης Δηικόων.

But an earlier narrative appears to make the two Erginoi one and the same. Pindar makes the son of Klumenos a figure who is also part of the Argonautic tradition:

Pind. Olympian 4.17-27

“I will not stain my story
With a lie. A test proves the worth of a man.
This rescued the child of Klumenos
from the dishonor of the Lemnian women.
He won the race in bronze armor
And said to Hypsipyle as he left with the crown:
“This is my speed:
My hands and heart are its equal. Sometimes gray hair
grows even on young men.”
thick, before the appointed time.
οὐ ψεύδεϊ τέγξω
λόγον· διάπειρά τοι βροτῶν ἔλεγχος
ἅπερ Κλυμένοιο παῖδα
Λαμνιάδων γυναικῶν ἔλυσεν ἐξ ἀτιμίας.
χαλκέοισι δ’ ἐν ἔντεσι νικῶν δρόμον
ἔειπεν ῾Υψιπυλείᾳ μετὰ στέφανον ἰών·
‘οὗτος ἐγὼ ταχυτᾶτι·
χεῖρες δὲ καὶ ἦτορ ἴσον. φύονται δὲ καὶ νέοις
ἐν ἀνδράσιν πολιαί
θαμάκι παρὰ τὸν ἁλικίας ἐοικότα χρόνον.’
A scholion to Pindar provides a little more information about this tale:

Schol.Pind. O4 32b-c
“This contest took the dishonor of the Lemnian women away from the son of Klymenos. The story goes like this: when Hypsipyle held funeral games for her father Thoas, the king of the Lemnians, it happened that the Argonauts appeared as they were sailing for the golden fleece and they offered to compete in the games. One of them, Erginos, was younger than old, but his hair was prematurely grey and he was taunted by the women for it. But he showed them in the deeds by defeating his competitors. They were the sons of Boreas, Zetes and Kalaïs.”

ἥτις διάπειρα τὸν Κλυμένου παῖδα ἀπέλυσε τῆς ἀτιμίας τῶν ἐν Λήμνῳ γυναικῶν.
ἡ δὲ ἱστορία τοιαύτη· ῾Υψιπύλης ἀγῶνα ἐπιτελούσης ἐπιτάφιον Θόαντι τῷ πατρὶ Λημνίων βασιλεῖ, συμβέβηκεν ἀπιόντας ἐπὶ τὸ χρυσοῦν δέρας τοὺς ᾿Αργοναύτας ἐκεῖσε γενέσθαι, καὶ προτραπέντας εἰς τὸν ἀγῶνα ἀγωνίσασθαι. εἷς ὢν οὖν αὐτῶν ὁ ᾿Εργῖνος νεώτερος μὲν τῷ χρόνῳ, προπόλιος δὲ τὴν κόμην, ὡς μὴ ἱκανὸς ἀγωνίσασθαι διὰ τὴν ὄψιν τῶν πολιῶν ἐγελᾶτο ὑπὸ τῶν γυναικῶν καὶ ἐπεκερτομεῖτο. ὡς δὲ διὰ τῶν ἔργων ἐδείχθη ὑπερβαλλόμενος τοὺς ἀγωνιστάς· ἦσαν δὲ οἱ τοῦ Βορέου παῖδες Ζήτης καὶ Κάλαϊς·

The geographer Strabo claims that Minyans were Argonauts, and also places Erginos in Orkhomenos (9.2.40)

“Next the poet recites the catalog of the Orkhomenians, whom he distinguishes from the Boiotian tribe. He calls Orkhomenos “Minyan” from the tribe of the descendants of Minyas. People say that some of the Minyans left there for Iolcus and that this is why the Argonauts are called Minyans. The city appears to be ancient and to have been wealthy and very powerful. A testament to this is Homer, too. For when he numbers the places that were very wealthy he says “not as much as arrives in Orkhomenos or Egyptian Thebes. Indicative of its power is the fact that the Thebans paid a tribute to the Orkhomenians and their ruler Erginos who they say was killed by Herakles. Eteokles, one of those who ruled in Orkhomenos, was first to show both wealth and power in building the shrine of the Graces, either because he took graces, bestowed them, or for both reasons he honored the goddesses there.”

῾Εξῆς δ’ ὁ ποιητὴς μέμνηται τοῦ τῶν ᾿Ορχομενίων καταλόγου, χωρίζων αὐτοὺς ἀπὸ τοῦ Βοιωτιακοῦ ἔθνους. καλεῖ δὲ Μινύειον τὸν ᾿Ορχομενὸν ἀπὸ ἔθνους τοῦ Μινυῶν· ἐντεῦθεν δὲ ἀποικῆσαί τινας τῶν Μινυῶν εἰς ᾿Ιωλκόν φασιν, ὅθεν τοὺς ᾿Αργοναύτας Μινύας λεχθῆναι. φαίνεται δὲ τὸ παλαιὸν καὶ πλουσία τις γεγονυῖα πόλις καὶ δυναμένη μέγα· τοῦ μὲν οὖν πλούτου μάρτυς καὶ ῞Ομηρος· διαριθμούμενος γὰρ τοὺς τόπους τοὺς πολυχρηματήσαντάς φησιν „οὐδ’ ὅσ’ ἐς ᾿Ορχομενὸν ποτινίσσεται, „οὐδ’ ὅσα Θήβας Αἰγυπτίας.” τῆς δυνάμεως δέ, ὅτι Θηβαῖοι δασμὸν ἐτέλουν τοῖς ᾿Ορχομενίοις καὶ ᾿Εργίνῳ τῷ τυραννοῦντι αὐτῶν, ὃν ὑφ’ ῾Ηρακλέους καταλυθῆναί φασιν. ᾿Ετεοκλῆς δέ, τῶν βασιλευσάντων ἐν ᾿Ορχομενῷ τις, Χαρίτων ἱερὸν ἱδρυσάμενος πρῶτος ἀμφότερα ἐμφαίνει, καὶ πλοῦτον καὶ δύναμιν, ὃς εἴτ’ ἐν τῷ λαμβάνειν χάριτας εἴτ’ ἐν τῷ διδόναι
κατορθῶν εἴτε καὶ ἀμφότερα, τὰς θεὰς ἐτίμησε ταύτας.

A scholion to Ap.Rhodes attempts to clarify the situation (several sources make Minyas a son of Poseidon):

Scholia to Ap.Rhodes 1.186

“One was the son, but Erginos was really a descendant. Angkaios was the son of Astupalaia, the Phoenician, and Poseidon. Erginos was the son of Klumenos, the son of Presbaon, and Bouzugê, the daugher of Lykos. He was Miletus…”

185—88a καὶ δ’ ἄλλω δύο παῖδε: ὁ μὲν ἦν υἱός, ὁ δὲ ᾿Εργῖνος ἀπόγονος· ᾿Αγκαῖος υἱὸς ᾿Αστυπαλαίας τῆς Φοίνικος καὶ Ποσειδῶνος, ᾿Εργῖνος δὲ Κλυμένου τοῦ Πρέσβωνος καὶ Βουζύγης τῆς Λύκου. ὁ δὲ Μίλητος, ἀφ’ οὗ καὶ ἡ πόλις Μίλητος…

I still haven’t figured out the Milesian connection. So expect more! But I am fairly confident that there really just was one Erginos…