For Banking Applications :
Banking applications are one of the most complex websites, from a testers point of view. They :
- Have loads of functionality (Money Transfers, Credit cards, Reports, Billing, Payments)
- Large Scale Integration- of the various functional modules listed above
- Complex Business Workflows
- Real time processing
- High rate of transactions
- Transactions that should be ultra-secure
- Tons of reporting
- Need a massive storage system
- Should be prone to disaster
So, when you say, that you want to devise a testing strategy, for a banking application, you need to keep the above points in mind and then design your tests and testing strategy accordingly.
When talking about a banking application, a testing strategy should, include end-to-end testing methodology, involving multiple software testing techniques. Your testing strategy should ensure that
- Total coverage of all banking workflows and business requirements is achieved.
- Key aspects like Security and Functional testing should assigned top most priority.
- Data integrity is maintained.
- User Acceptance/Experience should be good.
Keeping in mind, all the above core points, I would, hypothetically device testing scenarios that would include and cover the following testing :
- Integration Testing
- Functional Testing
- Database Processing/Storage
- User Acceptance and User Experience
Now, you have to go further down in the listed types (and these are not limited to this in any way), and design your test cases, to ensure the points mentioned above are covered.
This link by Guru99 website has a good number of scenarios listed for login in a banking application. You can take a reference from this.
Another good read is this.
For Payment Gateways :
Our very own and beloved Kate Paulk, has written a well explained post here : Payment gateways checklist
This should be enough to answer your queries.