Short answer
No, not in the Hanafi school. The small tuft between the lower lip and the chin (the anfaqah) is counted as part of the beard, and the Hanafi texts call plucking the hair on either side of it an innovation. You may trim it short enough that it does not get into your mouth.
The anfaqah is part of the beard, so shaving or plucking it takes the ruling of removing the beard. Al-Fatawa al-Hindiyya states that plucking the two sides of the anfaqah (the fanikayn) is bid'ah. Trimming hairs that cover the lip or touch food is allowed.
The four schools agree on this.
Explanation
When Abdullah ibn Busr was asked whether the Prophet ﷺ had grown old, he said there were a few white hairs in his anfaqah, the hair just under the lower lip. So he kept that hair, and the command to let the beard grow includes it.
The Hanafi books define the beard as the hair of the cheeks, the jaw and the chin, and they mention the anfaqah with it. Al-Fatawa al-Hindiyya says that plucking the fanikayn, the patches on either side of the anfaqah, is an innovation. Many men shave those patches to make a sharp soul patch or to separate the tuft from the chin. That is the practice the texts reject.
- Allowed: trimming the hair so it does not curl into your mouth or touch your food and drink. This is the same reason the moustache is kept short.
- Not allowed: shaving the tuft, shaving the patches beside it, or plucking it to shape it.
- Wudu: it is washed as part of the face. Run your wet fingers through it if it is thick.
A soul patch on its own with the rest of the face shaved is covered in is a goatee haram, and the general ruling in is shaving your beard haram. For the moustache above the lip see how to trim the moustache.
The evidence
Sahih al-Bukhari 3546
Sahih... كان في عنفقته شعرات بيض ...
"There were a few white hairs in his anfaqah."
Abdullah ibn Busr's description shows the Prophet ﷺ kept the hair under his lower lip.
Sahih al-Bukhari 5892
Sahih... خالفوا المشركين وفروا اللحى وأحفوا الشوارب ...
"Be different from the idolaters: let the beard grow fully and trim the moustache short."
The command to grow the beard, which the Hanafi school treats as wajib.
Where the ruling is recorded
- al-Fatawa al-Hindiyya, Kitab al-Karahiyya, chapter on circumcision, hair and nails. Plucking the two sides of the anfaqah is an innovation.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Taharah, on washing the face and the beard in wudu. The hair of the face and chin that is washed in wudu.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.