"I saw the Messenger of Allah (ﷺ) performing Wudu' and sprinkling his private area (with water)."
Sunan an-Nasa'i Book 1, Hadith 136
← Previous Hadith "He would sprinkle his private parts with it." Shaikh Ibn As-Sunni said: "Al-Hakam (one of the narrators) is Ibn Sufyan Ath-Thaqafi.

The purpose is to ward off devilish whispers lest the person think any emission has taken place, and thus think that his Wudu' has been invalidated.

Sunan an-Nasa'i Book 1, Hadith 135 Next Hadith → "I saw 'Ali performing Wudu', washing each part thrice. Then he stood up and drank the water that was left over from his Wudu' and said: 'The Messenger of Allah (ﷺ) did as I have done.'"

Sunan an-Nasa'i Book 1, Hadith 137