Hi, there's 2 ways to get an internship with a bank.
1) through a University as part of the final year project where students have to serve an internship
2) knowing someone influential in the bank so he/she can request for an internship on your behalf

From your field of studies, option 1 may not be possible as I understand the University may only arrange for banking internship for Business or Economics students. If you're able to find a source for option 2, great!

An internship with the bank doesn't necessary lead to an offer with the bank, nor is an internship necessary to get a job in a bank.

A lot of banks are hiring non-business degree holders nowadays, so don't worry if your degree is not business related. You can also try to apply for a management trainee role which gives you opportunity to learn/see different aspects of the bank.

For the area that you're interested in, it may be difficult to get in without experience, so do consider temp/contract roles which may give you an opportunity to get into the dept or a job rotation after you get into the bank through other dept.

Do note that you'll be starting from junior role so don't expect to be doing all the "impt and fun" stuff right from the start. Your colleagues would have built their knowledge from years of experience. So take the opportunity to learn from them. As a junior staff, you can ask lots of questions and people will still entertain them.

Good luck and all the best!