What is the ruling on working in a bank that conducts mixed activities (permissible and impermissible) if the job is only in the department of permissible activities and has no relation to the impermissible activities?

There is no harm in working for the aforementioned bank in this field. The fact that some of the bank's money is Haram (definition) does not affect the salary, as it is permissible to engage in permissible transactions with someone whose wealth is mixed. However, it is safer for a person to distance themselves from doubtful matters. And whoever fears Allah - He will make for him a way out and provide for him from where he does not expect.