Difference between final static and static final

No difference at all. According to 8.3.1 - Classes - Field Modifiers of the Java Language Specification,

If two or more (distinct) field modifiers appear in a field declaration, it is customary, though not required, that they appear in the order consistent with that shown above in the production for FieldModifier.

For fields, the said production lists the modifiers in this order:

@Annotation public protected private static final transient volatile

And for methods:

@Annotation public protected private abstract static final synchronized native strictfp

They are the same. The order of modifiers is not significant. And note that the same rule applies in all contexts where modifiers are used in Java.

However, most Java style guides recommend/mandate the same specific order for the modifiers. In this case, it is public static final.

private static final String API_RTN_ERROR= "1";
private final static String API_RTN_ERROR= "1";
static private final String API_RTN_ERROR= "1";
static final private String API_RTN_ERROR= "1";
final static private String API_RTN_ERROR= "1";
final private static String API_RTN_ERROR= "1";

even all above are same the position of first three is intercangeable.

They are same,

private final static String API_RTN_ERROR = "1";

private static final String API_RTN_ERROR= "1";

What is the difference between them or are they same?

If you are talking about changing order of static and final then yes they are same.

does it differ for private or public?

No, you can use any order in private and public. Just difference is private variables will not be accessible outside of class directly.