In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Answering your question, The Fatwa Center at Islamweb, states:
Biting the nails does not break one’s fast unless parts of the nails are swallowed deliberately. However, a Muslim should stop this act because it might harm one’s health, as specialist doctors say. It was authentically narrated on the authority of Ibn ‘Abbas (may Allah be pleased with him) that the Prophet (peace be upon him) said: “[Let there be] no harm, nor the reciprocation of harm.” (Ahmad and Ibn Majah)
Almighty Allah knows best.