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If a 6th-level Draconic Bloodline sorcerer with Elemental Affinity (fire) casts Green-Flame Blade, is only the first target's damage increased, or both?

The Elemental Affinity feature (PHB, p. 102) says:

[...] when you cast a spell that deals damage of the type associated with your draconic ancestry, add your Charisma modifier to that damage.

The description of the Green-Flame Blade cantrip (SCAG, p. 143) says:

[...] the target suffers the attack’s normal effects, and green fire leaps from the target to a different creature of your choice that you can see within 5 feet of it. The second creature takes fire damage equal to your spellcasting modifier.

[...] At 5th level, the melee attack deals an extra 1d8 fire damage to the target, and the fire damage to the second creature increases to 1d8 + your spellcasting ability modifier.

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You can only add your Charisma modifier once: "when you cast a spell ... add your Charisma modifier ...". However, you can choose (before rolling damage) if the primary or secondary target suffers the extra damage. A kind DM (like me) may even let you split the extra damage as you desire.

Naturally, Elemental Affinity is more effective on area of effect spells (Burning Hands, Fireball etc.) where even though the extra damage is added only once it can affect multiple creatures.

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Either, but not both.

Per The Player's Handbook Errata,

Elemental Affinity (p. 102). The damage bonus applies to one damage roll of a spell, not multiple rolls.

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Before the errata, it applied to both targets: it’s one spell, like scorching ray, hitting multiple targets, so it applies to the entire spell. In fact that’s why it can’t be twinned.

After the errata, it only applies to one roll, but you choose which, same as scorching ray.

If this isn’t an AL character do yourself a favour and grab divine sorcerer instead. A quickened spirit guardians which scales extremely well with spell slots will serve you much better if your table uses the errata.

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