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The Vampiric Bite, from the Dhampir lineage race in the January 2021 Unearthed Arcana, says as follows (emphasis mine):

Vampiric Bite

"Your fanged bite is a natural weapon, which counts as a simple melee weapon with which you are proficient. You add your Constitution modifier to the attack and damage rolls when you attack with your bite. Your bite deals 1d4 piercing damage on a hit. While you are missing half or more of your hit points, you have advantage on attack rolls you make with this bite."

Normally, a simple melee weapon attack works as follows:

Attack Rolls

To make an Attack roll, roll a d20 and add the appropriate modifiers.

Modifiers to the Roll

Ability Modifier The ability modifier used for a melee weapon Attack is Strength, and the ability modifier used for a ranged weapon Attack is Dexterity.[...]

Proficiency Bonus You add your Proficiency Bonus to your Attack roll when you Attack using a weapon with which you have proficiency, as well as when you Attack with a spell.

This translates into rolling 1d20 + STR modifier + Proficiency bonus.

Does it mean that a Vampiric Bite attack adds CON modifier to the above formula (1d20 + STR mod + Proficiency bonus + CON mod)?

Same question for the damage roll:

Damage rolls

When attacking with a weapon, you add your ability modifier—the same modifier used for the Attack roll—to the damage.

Normally for a melee weapon the attack formula is [weapon-damage-die] + STR modifier. If another modifier is used, instead of the usual one, the wording is different from what we see in the Vampiric Bite. An example is Finesse weapons, which say as follows:

Finesse

When Making an Attack with a finesse weapon, you use your choice of your Strength or Dexterity modifier for the Attack and Damage Rolls. You must use the same modifier for both rolls.

Is it correct to say that, unlike Finesse weapons, the Vampiric bite does not replace the STR modifier with CON, but rather adds both (making the damage formula 1d4 [weapon-dmg-die] + STR modifier + CON modifier)?

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    \$\begingroup\$ I added the link to the UA this race is from. This is both for the benefit of those who missed it, but also in case it is republished with changes (either in UA or book). \$\endgroup\$
    – Someone_Evil
    Feb 6, 2021 at 12:24

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This issue has apparently been fixed in the official version found in Van Richten's Guide to Ravenloft where the wording specifically says

You add your Constitution modifier, instead of your Strength modifier, to the attack and damage rolls when you attack with this bite. It deals 1d4 piercing damage on a hit.

This means it would be Con Mod + Prof to attack and 1d4 + Con mod as the damage.

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Congratulations!

You have discovered some valuable feedback for this play test material! You should share it via the Unearthed Arcana feedback system.

Text

The text supports your interpretation of adding two ability score modifiers to attacks with the vampiric bite. Which is unprecedented, over powering, and makes dhampir barbarians really appealing.

Intent

It seems clear that the intent of the rules was CON instead of STR. However, that is not what the rules say, and rules say what they mean in 5E.

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    \$\begingroup\$ @Odo Finesse also uses "instead of", as noted by the OP. It might be construed as insulting, so I chose not to mention such examples. \$\endgroup\$
    – ValhallaGH
    Feb 6, 2021 at 16:34
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    \$\begingroup\$ And as it happens, when it was finally published, the wording became "You add your Constitution modifier, instead of your Strength modifier, to the attack and damage rolls when you attack with this bite." making it 100% clear you add only Con, not Str. \$\endgroup\$ Dec 8, 2021 at 16:28

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