Wherever you got a spell from, use that Spellcasting Modifier
For a starting point--let's look at the more common way of having multiple spellcasting modifiers, Multi-classing. From the Basic Rules, we have this on Multiclass Spellcasting
Each spell you know and prepare is associated with one of your classes, and you use the spellcasting ability of that class when you cast the spell.
Thus, if you were a Cleric/Wizard...any spells you gained from the Cleric Class would use Wisdom, any spells you gained from the Wizard Class would use Intelligence.
This same basic understanding extends into races that give you spellcasting. For example, the Tiefling:
Charisma is your spellcasting ability for these spells.
Or the newer ones that let you pick, like the Air Genasi
Intelligence, Wisdom, or Charisma is your spellcasting ability for these spells when you cast them with this trait (choose when you select this race).
Emphasis mine, in both cases. Now, the fact that you're using a creature from the Monster Manual as your race means that it doesn't have this exact phrasing--just like a homebrew race may not have such standardized phrasing, but the intent is clear.
Spells gained (or known, or prepared) from Source A use the spellcasting ability of Source A.
Therefore, in your particular case, spells gained from your 'Fae Dragon' race would be cast using your Fae Dragon spellcasting ability. Spells gained from and prepared through the rules of your Wizard class will use your Wizard spellcasting ability.