Date and time conversion to some other Timezone in java

SimpleDateFormat#setTimezone() is the answer. One formatter with ETC timezone you use for parsing, another with UTC for producing output string:

DateFormat dfNy = new SimpleDateFormat("yyyy-MM-dd HH:mm:ss", Locale.ROOT);
dfNy.setTimeZone(TimeZone.getTimeZone("EST"));
DateFormat dfUtc = new SimpleDateFormat("yyyy-MM-dd HH:mm:ss", Locale.ROOT);
dfUtc.setTimeZone(TimeZone.getTimeZone("UTC"));

try {
    return dfUtc.format(dfNy.parse(input));
} catch (ParseException e) {
    return null;              // invalid input
}

Your mistake is to call parse instead of format.

You call parse to parse a Date from a String, but in your case you've got a Date and need to format it using the correct Timezone.

Replace your code with

Calendar currentdate = Calendar.getInstance();
DateFormat formatter = new SimpleDateFormat("dd-MM-yyyy HH:mm:ss");
TimeZone obj = TimeZone.getTimeZone("CST");
formatter.setTimeZone(obj);
System.out.println("Local:: " +currentdate.getTime());
System.out.println("CST:: "+ formatter.format(currentdate.getTime()));

and I hope you'll get the output you are expecting.

It's over the web. Could have googled. Anyways, here is a version for you (shamelessly picked and modified from here):

Calendar calendar = Calendar.getInstance();
TimeZone fromTimeZone = calendar.getTimeZone();
TimeZone toTimeZone = TimeZone.getTimeZone("CST");

calendar.setTimeZone(fromTimeZone);
calendar.add(Calendar.MILLISECOND, fromTimeZone.getRawOffset() * -1);
if (fromTimeZone.inDaylightTime(calendar.getTime())) {
    calendar.add(Calendar.MILLISECOND, calendar.getTimeZone().getDSTSavings() * -1);
}

calendar.add(Calendar.MILLISECOND, toTimeZone.getRawOffset());
if (toTimeZone.inDaylightTime(calendar.getTime())) {
    calendar.add(Calendar.MILLISECOND, toTimeZone.getDSTSavings());
}

System.out.println(calendar.getTime());