What is the expiation for taking an amount of 1300 Saudi Riyals that was refunded after renewing the residency permit via an ATM, and how is this amount to be returned?

The expiation for what you have done after repenting to Allah, the Almighty, the All-Glorious, is to return the money to its owners, based on the hadith: "On the hand is what it took until it returns it." So, if you know who the rightful owner of the money is, then pay it to him. By doing so, you will clear your conscience.