Ash Crimson/Story

Past
Ash is the descendant of Saiki. When he was living in France, he spent his childhood years with Elisabeth Blanctorche. For reasons still not entirely divulged, he left her household and the Blanctorche teachings.

The King of Fighters 2003
Ash enters the 2003 edition of The King of Fighters tournament alongside Duo Lon and Shen Woo. While his teammates leave him to solve their own vendettas, Ash goes to the Orochi seal where Kyo, Chizuru, and Iori are investigating. Ash ambushes a weakened Chizuru, robs her powers, and leaves her unconscious. He taunts that Iori will be next before fleeing from the scene.

The King of Fighters XI
Ash enters the next tournament with Shen and Oswald. After the tournament's events, he reveals to Oswald that Shen is the target he has been contracted to assassinate, a set up that Ash had in place before the tournament occurred. After leaving his teammates to fight amongst themselves, Ash takes advantage of Iori's unstable Riot of the Blood state to steal the Yasakani Jewel. Before he leaves the tournament grounds, Elisabeth Blanctorche and her team appears before him. She accuses Ash of abandoning "their mission" and fighting for personal gain. To intimidate her, he unleashes his new purple flames and disappears using the Yata Mirror. He warns them that Kyo is next.

The King of Fighters XIII
Prior to the KOF XIII tournament, Ash openly joins forces with Those from the Past and works for their master. During the tournament finals, his true motives are revealed: his previous actions were done to earn Saiki's trust and to gain enough power to rob Saiki's soul. He wants to end their bloodline. Ash carries out his true plan when Saiki finally lowers his guard, but Saiki's essence overwhelms him.

After being defeated again by the winning team, Ash regains control of his body. Saiki insists that Ash enter the Time Gate, which will allow them to return to a previous era and begin their entire plan over again. Since Ash likes the current world, he allows the gate to close. His inaction erases both him and Saiki from time. Ash has a few moments to apologize to Elisabeth before disappearing. He leaves the stolen sacred treasures behind for Iori and Chizuru to reclaim.

The King of Fighters XIV
As implied by Nakoruru, Ash Crimson's act of erasing Saiki (and consequentially, his own self) from existence by orchestrating a temporal paradox (by trapping Saiki in the present time) sets up the events in the game, and resulted in the appearance of the entity known as Verse.

After Verse's defeat, Ash's soul is released and is found by Kukri and Elisabeth on Carpathian Mountains in Ukraine. While he is still in coma-state, Ash is confirmed alive again.

The King of Fighters XV
His canon appearance here ultimately confirms his revival from being erased from existence previously.