Messmer's red hair and Fire Knights
One of the most compelling pieces of evidence for fans supporting the theory of Messmer being one of Radagon's children is his red hair. It doesn't surprise the color of the demigod's hair apparently represents such a highly effective proof, considering the game subtly implies that red hair is a rarity in the Lands Between: red hair is a distinctive trait of the Fire Giants, and the only other beings having hair of this same color are Radagon and his children. Therefore, it makes sense to think Messmer's hair are the undeniable proof of this supposed family connection between the Impaler and the red-haired champion.
However, there's a little detail that many haven't noticed, included me at first: Messmer's Fire knights also have red hair.
...well, isn't this confusing as heck.
Obviously they cannot be other children of Radagon, after all the descriptions of their set states they were former nobles of the Erdtree society (so we aren't talking about royalty either). Still, they have red hair, just like their master... and guess what, they are the only knights, among all the soldiers of Messmer's army, knowing about the demigod's true serpentine nature and, more importantly, the only ones Messmer shared his flame with.
Incantation of the Fire Knights under Messmer the Impaler's personal command*. Launches a flame with a serpentine coil. Charging enhances potency.*
When the flame they received from Messmer would not find purchase within them, the Fire Knights relied on fire incantations to honor their bond.
(Fire serpent's description)
In short, they share the power of their master's flame and hold this same flame inside them, although it "would not find purchase within them.
Helm of Kood, captain of the Fire Knights. A winged serpent perches atop it. Enhances Fire Knight skills. The winged serpent is the token creature of Messmer's military forces. It is a wise friend which keeps the base serpent at bay and holds its power in check*.*
(Winged Serpent helm's description)
And so, what if the red color of Messmer's hair, instead of stemming from a supposed blood relationship with Radagon, comes from the flame dwelling inside him? That would explain why his Fire knights have his same hair color, having the same flame inside their body. Retrospectively, maybe this would also explain why all Fire Giants have red hair, being worshippers of the Fell God and harboring it inside their torso.
... or maybe the Fire knights just wanted to dye their hair because they're a big happy Messmer fanclub, who knows :p