Zakaat on jewellery that was gifted to one by one's parents

If your parents bought it for you before you became baaligh, or they gifted it to you before you became baaligh, then your possession was not required. You will be regarded as the owner of the jewellery, even though you did not yet take possession of it. In this case, zakaat will be compulsory upon you for the jewellery from the time you became baaligh. If your parents pay the zakaat for you after taking your consent, the zakaat will be discharged.

However, if they gifted it to you after you became baaligh, then the gifting will only be valid once you take possession of it. If you did not take possession of it, then you did not become the owner of the jewellery, and zakaat is not compulsory upon you for the jewellery.

And Allah Ta'ala (الله تعالى) knows best.