Reference: Fataawa Noor ‘alad-Darb – Question No.5734, Page 186, Volume 11
Question: In your opinion, what is the ruling about wearing a watch on the left wrist; is there any harm [in doing so]?
Response: There is no harm in wearing a watch on the left wrist, [as] there is no [legislated] preference in [this matter]. So you have a choice between wearing it on the right wrist or the left one. And it has been [authentically] reported that the Prophet ﷺ would sometimes wear a ring on the right hand, and sometimes on his left hand, and [the matter of] wearing a watch is similar to wearing a ring. So based upon this, we say whoever wears it on the left [wrist] then there is no harm in that, and whoever wears it on the right [wrist], then there is no harm in that [either]. [In short], there is no preference in one over the other.