(picture above is from the arcane artbook, it's concept art for Mel, Kino, Ambessa and Kino's unnamed father. Mel's father isn't named or shown anywhere yet)
I don't think Arcane necessarily retconned this, so I wanted to talk about the Medarda Clan in the League of Legends Universe.
Mel Medarda, while banished from Noxus, likely still retained a high status because a part of the Medarda family also resides in Piltover.
It makes sense that Medarda family members don't just reside in Noxus. Ambessa says herself that she send Mel to Piltover in order to oversee their family's interests. And would it really be called "Medarda House" by Piltover residents if only Mel is in it? Mel would have also been only about 23 when she enters Piltover and 26 when she was a councelor in season 1 act 1 (here is a timeline I made for arcane: x) it's insane, even for her, to establish a well respected house in such a short time in Piltover.
In Legends of Runeterra (a Riot card game that explores the world of Runeterra in more detail), there is a card named Jae Medarda.
His description reads: "Heir apparent to Piltover's prestigious Clan Medarda, Jae preferred hunting ancient artifacts over managing the family business... much to his father's chagrin."
There also some other Medarda family members that we know of; on the League website you can find a map named "Medarda Heirloom", it shows trading routes the Medarda's use. It's a pretty old map though, I think it's from 2016 so I wouldn't really say this very relevant.
On the map you can find a letter by a Medarda Merchant named Jago writen to his nephew, Salob, who seems at risk of being banished.
I tried my best to make out every word:
As much as I am forced to admire your frankly staggering & baffling level of self-belief in the face of numerous failures, failures that would have punctured the ego of the staunchest Zaunite braggart. I would like to confirm, in writing, that control of the Medarda Clan's commerical portfolio and access to the clan trade map. Which you have long coveted, shall not be granted to you - not now - not in time - nor never.
I suggest you take on a profession more befitting your natural talents - perhaps as a chem-lamp lighter - and be grateful to your aunt, my dear wife, that your ties with the clan are not severed completly.
This will be the end of the matter.
The Medarda family seems to love exiling children that don't fit into the family.
I think Jago is now kind of retconned if Arcane is the new canon, or he's at the very least not the head of the clan and has married into the family. Sun Gates are what made a lot of the families in Piltover rich 200 years ago, it's not mentioned in arcane but we do see them in some arcane maps.
In Arcane Ambessa mentions that she fought battles from the Bloodcliffs to the Dalamor Plains. The Black Rose mentions that she might have had an affair while travelling through Basilich, at least fake-Kino claims that this is the area he heard rumors about Ambessa's affair in. I marked all these places with a red dot on the Runeterra map. Basilich is a Port City, if the affair really did happen here, Mel's father could be from any place in Runeterra.
I'm hoping they will expand on the Medarda family in the future, the Ambessa book will likely have some interesting lore about them in it. It comes out in Feb 2025.
From the Synopsis we already know that there will be a cousin of Ambessa that is named Ta’Fik. I'm guessing he knows that Ambessa had an affair and has bad blood with the Black Rose.
Ambessa Medarda: Warrior, general, mother. She is a woman to be feared, and the Medardas are unrivaled in their pursuit of glory. She has led conquests and armies. She has slain legendary beasts. She has made grave sacrifices in her ascent up the ranks. And for this she was rewarded: She entered the realm of death and was granted a vision of herself upon the throne of the vast Noxian empire.
But before she can lead her empire, she must become head of her own clan. Yet the title is contested by her cousin and former confidante, Ta’Fik. He knows the bloody sins of Ambessa’s past. And he knows he cannot allow her to rise.
They will fight a war for the very soul of the Medardas.
But the war won’t be fought on battlefields alone. Ambessa’s daughter, Mel, can deftly break through the walls around anyone’s heart, and she’ll put her talents to use for her mother. Yet despite Mel’s strength, Ambessa sees only a child who lacks her killer instincts. Mel knows she can be the leader Ambessa wants her to be, if only she gives her time.
With her family betraying her, enemies closing in on all sides, and unseen forces moving in the shadows, every day proves more dangerous than the last. But Ambessa will not bow. She will burn the world down to claim her place in it.