Since you have completed BE, have you given thoughts about the GATE exams, if you have a good score, you can get into the public and private sector or even a teaching career.
If you are keen only on a banking job, then you need to have a shot at the IBPS exams.This gives you a chance to enter as a probationary officer.
These exams are highly competitive with lakhs of applicants each year. Apart from a degree, you need good computer skills and command (verbal and written) language of the state. These exams have the preliminary and the main exams with the focus on reasoning ability, aptitude, data analysis, and interpretation. The papers have a negative marking of 0.25 marks. Then you have the final round of interview.
So, you need have a good coaching and preparation for the IBPS. There are a lot of sites, apps and coaching centers to guide you apart from books and mock exams. Many sites offer you guidance and training (http://nsbindia.net). Once you clear this, you have an opening in the public sector banks, LIC, and private sector banks.
Once you clear, then you can join the vacancies listed. The private sector also requires candidates after their IBPS, although not mandatory. In the private sector, the job spectrum is more wide, based on your core skills and interests you can choose retail banking, credit, assets, sales, payment or relationship management. You can complete a PG course or a diploma in corporate governance, finance, international banking and then try international jobs.
Retail banking academy in London is an academy that has a global retail banking certification program. It also has a scholarship program for people who perform well in the Indian banks with three-year experience. (https://www.retailbanking-academy.org/ccppscholarshipindia).
ICICI has regular jobs, sales management programm and probationary officer programs. It also offers career counseling (https://www.icicicareers.com/website/careers/career-counselling/2017/Aug/career-counselling.html).