All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Since your account is in an Islamic bank and you only withdraw money from your account balance, then there is no sin in this, whether you withdraw through the ATM of the Islamic Bank or other banks. There is no sin because of the fees that are deducted by the bank for the card service when withdrawing from ATM machine of other banks. This is so if these fees represent an actual fee for services provided to the cardholder.
If the ATM card is used to withdraw money from ATM machine of other banks, then the bank that issued the card will transfer the amount that was withdrawn to the bank from which the amount was withdrawn, so they are entitled to take a fee for that service.
Additionally, ATM machines belong to international companies who take a fee to rent out these machines, so the bank has the right to take a fee for facilitating the service of withdrawing from it. However, some banks may provide this service free of charge to their customers to commercially compete with other banks.
The Fatwa and Sharee’a Supervisory Board in the Kuwaiti Finance House and the Fatwa of Al-Barakah Seminar, and some researchers such as Dr. Abd As-Sattaar Abu Ghadah and Dr. Mohammad Mokhtar As-Salaami, issued a Fatwa that it is permissible to take fees for withdrawals through ATMs, whether it is a percentage of the amount withdrawn, or a lump sum. This is because the fees are in exchange for services provided by the bank issuing the card, such as delivering the money to the cardholder anywhere through its branches or ATMs. These fees are also in exchange for services provided by the bank from which the money is withdrawn, such as making calls, telegraph fees, exchange devices, and so on.
For more benefit, please refer to Fataawa 30077 and 89479.
Allah knows best.