Those who did not wear a ring

Abd al-A'la bin Abdullah said: I asked Sa'id bin al-Musayyib: A man has on his ring a picture like the head of a bird. What is the ruling on it? He said: O son of my brother, we do not know of any Companion of the Messenger of Allah (peace and blessings be upon him) who wore a ring: not Sayyiduna Abu Bakr (may Allah be pleased with him), nor Sayyiduna Umar (may Allah be pleased with him), nor so-and-so, nor so-and-so. He named many Companions of the Messenger of Allah (peace and blessings be upon him). I asked him again, and from his answer I gathered that he considered it disliked.

Ata, Tawus and Mujahid did not wear rings.