Q: will there be any issue for my system if I upgrade my database which is oracle 11.1.0.6 to 11.1.0.7 I'm working on Oracle 11.1.0.6 and planning to upgrade it to 11.1.0.7. What are the expected issues I'm going to face? P.S: it's for banking system

A: Test it is the answer. Minor upgrades should not give problems but if you do not test your application you will not be sure.

A: 11.1.0.7 is so far out of support that it's not even funny (end of support was August 2015 for "extended" support - see http://www.oracle.com/us/support/library/lifetime-support-technology-069183.pdf).
Given that you will (presumably) be doing a full-scale regression test for any upgrade of this scale, why choose to land on an unsupported version, when you could move to a supported version?
It'd be a two-step upgrade for you (11.1.0.6->11.1.0.7->12.1.0.2), but long-term, it's a better position to be in.
To directly answer your question, you'll find out what issues you'll face by doing a full regression test.  That's the only way.
