Validating multiple EditText fields
The warning is trying to tell you that the return is pointless,
because it's the last statement anyway.
Here's a better way to rewrite that,
which will make the warning naturally go away:

if (!pwd.equals(pwd1)) {
    onShake(edt_password, "Passwords do not match");
    onShake(edt_password1, "Passwords do not match");
    return;
} 

startbackgroundtask("formBased");


I simply inverted the condition, and removed the else branch.
If you think about it, all the else branches are unnecessary when the if branch returns. You can apply this to all the conditions in the posted code.



Many of your conditions handle the invalid case in the if and the normal case in the else, but not all.
It would be better to consistently handle the invalid case first everywhere,
and use early returns so you can get rid of the else. Like this:

    if (TextUtils.isEmpty(edt_name.getText().toString().trim())) {
        onShake(edt_name, "Please enter a valid name");
        return;
    }
    name = edt_name.getText().toString().trim();

    if (!isValidEmail(edt_email.getText().toString().trim())) {
        onShake(edt_email, "Please enter a valid email ID");
        return;
    }
    email = edt_email.getText().toString().trim();

    if (((edt_password.getText().length() &lt; 6) || (TextUtils.isEmpty(edt_password.getText().toString().trim())))) {
        onShake(edt_password, "Password must be at least six characters long");
        return;
    }
    pwd = edt_password.getText().toString().trim();

    if (TextUtils.isEmpty(edt_password1.getText().toString().trim())) {
        onShake(edt_password1, "Not valid");
        return;
    }
    pwd1 = edt_password1.getText().toString().trim();

    if (!pwd.equals(pwd1)) {
        onShake(edt_password, "Passwords do not match");
        onShake(edt_password1, "Passwords do not match");
        return;
    }

    startbackgroundtask("formBased");




Notice that the code contains many duplicated logic, for example here,
the code to extract and clean edt_name is written twice:

    if (TextUtils.isEmpty(edt_name.getText().toString().trim())) {
        onShake(edt_name, "Please enter a valid name");
        return;
    }
    name = edt_name.getText().toString().trim();


It would be better to rewrite without duplication, like this:

    String cleanedName = edt_name.getText().toString().trim();
    if (cleanedName.isEmpty()) {
        onShake(edt_name, "Please enter a valid name");
        return;
    }
    name = cleanedName;


I also removed TextUtils.isEmpty, which was either a bug or pointless:


It's a bug if edt_name can be null, or if edt_name.getText() might return null: in both of these cases you will get a NullPointerException
If there won't be nulls, then you don't need TextUtils, you can use isEmpty method of String




There are several elements of poor coding style:


Variable names and method names should be camelCase, not like "edt_name" or "clientsideauth"
pwd and pwd1 are also poorly named, since pwd is the first password and pwd1 is the second. pwd1 and pwd2, or even pwd and pwdConfirmation would have been even better.




The clientsideauth method is doing too much:


Validate input
If successful, start background task
It mutates variables defined outside the method


Instead of mutating variables defined outside,
it would be better to validate,
collect the cleaned values in local variables,
and then pass these variables to the authentication task.



Since you do .getText().toString().trim() so often,
a helper method to do this for you would be a good idea,
to reduce your typing and the noise for readers.