It was narrated from Al-Hakam, from his father, that when the Messenger of Allah ﷺ performed Wudu', he would take a handful of water and do this with it. Shu'bah described it:

"He would sprinkle his private parts with it." [1]
Shaikh Ibn As-Sunni said: "Al-Hakam (one of the narrators) is Ibn Sufyan Ath-Thaqafi.

[1] 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.

أَخْبَرَنَا إِسْمَاعِيلُ بْنُ مَسْعُودٍ، قَالَ حَدَّثَنَا خَالِدُ بْنُ الْحَارِثِ، عَنْ شُعْبَةَ، عَنْ مَنْصُورٍ، عَنْ مُجَاهِدٍ، عَنِ الْحَكَمِ، عَنْ أَبِيهِ، أَنَّ رَسُولَ اللَّهِ ﷺ كَانَ إِذَا تَوَضَّأَ أَخَذَ حَفْنَةً مِنْ مَاءٍ فَقَالَ بِهَا هَكَذَا - وَوَصَفَ شُعْبَةُ - نَضَحَ بِهِ فَرْجَهُ فَذَكَرْتُهُ لإِبْرَاهِيمَ فَأَعْجَبَهُ قَالَ الشَّيْخُ ابْنُ السُّنِّيِّ قَالَ أَبُو عَبْدِ الرَّحْمَنِ الْحَكَمُ هُوَ ابْنُ سُفْيَانَ الثَّقَفِيُّ رضى الله عنه .