Yes, the Prophet Muhammad (peace be upon him) did wear a ring.
Historical accounts indicate that the Prophet (peace be upon him) used to wear a signet-ring. There are narrations that mention him wearing it on both his right and left hands.
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Different Narrations: Some narrations state he wore it on his right hand, while others say he wore it on his left. For example, one narration states, "The Prophet (peace_be_upon_him) used to wear the signet-ring on his right hand." Another narration mentions, "The Prophet (peace_be_upon_him) used to wear the signet-ring on his left hand, and put its stone next the palm of his hand."
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Significance: The ring served as a seal, likely used for authenticating documents and letters.
Therefore, based on various narrations, it is confirmed that the Prophet (peace be upon him) wore a ring, although the specific hand on which he wore it has varying accounts.