File screenshotFile=((TakesScreenshot)driver).getScreenshotAs(OutputType.FILE);
String file = String.format("Screenshots%s%s%s.png", System.getProperty("file.separator"), obj, GetTimeStampValue());
// check to see if the directory Screenshots exists, if not, create it.
FileUtils.copyFile(screenshotFile, new File(file));
Concatenating strings the way you are is not very efficient. It is better to use String.format to build a string from the other parts. Additionally, your code assumes a file separator is \ but this is only true for Windows. If you use the property file.separator this will work on non-Windows machines as well.
I put a comment in about creating the Screenshots directory if it doesn't already exist. As part of creating this directory you can also check for things like permissions and security. It is possible that the user you are running the tests under does not have write permission on the directory specified.
Also, I'm assuming GetTimeStampValue() returns a string. If it returns a int or long, change the last %s in the format string as necessary.