The incorrectly spelled word is "Adrointness."

The correct spelling is "Adroitness," which refers to skillfulness, agility, or dexterity in physical or mental tasks.

The other options, "Sinister," "Dexterous," and "Gauche," are spelled correctly and have the following meanings:

• Sinister: Means giving the impression of harmful, evil, or threatening intentions.
• Dexterous: Describes someone who is skillful or adept in performing tasks, especially with the hands.
• Gauche: Refers to someone who lacks social grace or tact, awkward or clumsy in social situations.