How does my mother pay Zakat for previous years for the commercial shop for which Zakat was not paid?

If the premises are commercial, your mother is obligated to pay zakat on trade goods if they reach the nisab (minimum threshold) and a hawl (one lunar year) passes over them. However, the building itself is not subject to zakat. If the premises are rented out, she is obligated to pay zakat on the rent if it reaches the nisab and a hawl passes over it. There is no zakat on the building itself.

If your mother has not paid zakat for past years, she must estimate the years and the funds for which zakat was not paid and then discharge the zakat due on them, in accordance with the Almighty's saying: "Allah does not burden a soul beyond its capacity." She must also repent if she delayed paying zakat while being aware of its obligation.