One option is to convert both of them to either lowercase or uppercase:

"Session".toLowerCase().startsWith("sEsSi".toLowerCase());

Another option is to use String#regionMatches() method, which takes a boolean argument stating whether to do case-sensitive matching or not. You can use it like this:

String haystack = "Session";
String needle = "sEsSi";
System.out.println(haystack.regionMatches(true, 0, needle, 0, needle.length()));  // true

It checks whether the region of needle from index 0 till length 5 is present in haystack starting from index 0 till length 5 or not. The first argument is true, means it will do case-insensitive matching.

And if only you are a big fan of Regex, you can do something like this:

System.out.println(haystack.matches("(?i)" + Pattern.quote(needle) + ".*"));

(?i) embedded flag is for ignore case matching.