Both "yes" and "no".
It is not prescribed in Qur'an or hadith.
Rather, it is a cultural or regional symbol. The hand as a protective symbol predates Islam and is not limited to Muslims, for instance, Jews also use the hand symbol, and some people call it the "Hand of Mary".
However some Shi'is have given it religious significance by using it to represent the ahl al-kisa'/panjtan (Muhammad, 'Ali, Fatimah, Hasan, and Husayn) and have used it to symbolise the intercession or protection of Hazrat Fatimah (A). In that way, it can symbolise her status and importance.
Possibly, it acquired this symbolism related to Hazrat Fatimah (A) and the panjtan during the Fatimid (Isma'ili) dynasty in North Africa (c. 10th-12th centuries CE).
Since, from ancient times, the symbol was often worn to protect mothers during childbirth, or to protect young children from the evil eye, this may be one reason why it was associated with a female figure. Maybe associating it with Fatimah also reflects hope in her motherly care since she is also often seen an archetypal mother figure, similar to the Virgin Mary.
However, some Shi'is also call it the Hand of 'Abbas due to what happened in Karbala and use it to represent similar things, such as honoring him, and seeking intercession and protection.
Some Sunnis also refer to it as the "Hand of Fatimah".
So, in short, the significance of it among Shi'is (or Muslims) is due to cultural practices that have developed over time to reflect religious ideals, in conjunction with the existing regional culture, rather than things that are prescribed in Qur'an or hadith.