That’s an error in the bank’s Java application, or an incompatibility between the app and the installed version of Java. Or both.
See what Java JDK is required for the banking app. Acquire and install that, downloading it from Oracle.
As for the older versions of Java, Java 6 cannot make a secure SSL/TLS network connection. It’s just too old. (Hopefully no financial institution is still requiring something that old, too.)
The newer versions of Java can require you to reconfigure the JDK, or to purchase a commercial license from Oracle. This depending on what parts of Oracle you're using. See the license agreement text for details.