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The description of the green-flame blade cantrip (SCAG, p. 143) says:

As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell's range, otherwise the spell fails. On a hit, 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 ability modifier.

Say you have a negative spellcasting ability modifier; for instance your spellcasting ability is Intelligence, and you have a -1 Intelligence modifier. You cast green-flame blade (and your character is below 5th level). How much damage does the second creature take? None, -1, or round off to 1 damage?

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Zero

The rules for damage state:

Damage Rolls

Each weapon, spell, and harmful monster ability specifies the damage it deals. You roll the damage die or dice, add any modifiers, and apply the damage to your target. Magic weapons, special abilities, and other factors can grant a bonus to damage. With a penalty, it is possible to deal 0 damage, but never negative damage.

You can't do -1 damage. You can do 0 damage. You don't round up to one unless you run across some damage source which specifically says to do so.

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The second creature would take no damage. From the SRD (under Damage Rolls, page 96):

With a penalty, it is possible to deal 0 damage, but never negative damage.

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