You just need to ask your mother to fill out the application materials for the supplementary card, and then you can sign it yourself and give it to the service staff of the bank.
However, I need to remind you that the main card and the auxiliary card of the credit card are shared, and the auxiliary card also needs to charge an annual fee, which is generally 50% of the main card. The specific rules for annual fee exemption are the same as those for the main card.
But the advantage of the secondary card is that the secondary card can also help the main card to merge together.