Return function Javascript

I saw on different posts callback function but it doesn't work for what I want to do.

Yes it does, you just need to change the way you think about code. Instead of writing email_already_exists_in_mysql you should instead write a function called if_email_already_exists_in_mysql:

/* Executes callback if email
 * already exists in mysql:
 */
function if_email_already_exists_in_mysql (email,callback) {
    connection.query(
        'SELECT COUNT(*) AS nb FROM user WHERE emailUser = ' +
        connection.escape(email),

        function(err, rows, fields) {
            if(rows[0].nb != 0) {
                callback();
            }
        }
    )
}

Then instead of writing this:

//If the email hasn't a good format
if(email_not_good_format()) {
    //I do something
}
else if(email_already_exists_in_mysql(email)) {
    //I do something
}

you write it like this instead:

//If the email hasn't a good format
if(email_not_good_format()) {
    //I do something
}
else {if_email_already_exists_in_mysql(email),function(){
    //I do something
})}

Now, you may ask yourself, what if there is another else after that? Well, you need to modify the if_email_already_exists_in_mysql function to behave like and if...else instead of just and if:

function if_email_already_exists_in_mysql (email,callback,else_callback) {
    connection.query(
        'SELECT COUNT(*) AS nb FROM user WHERE emailUser = ' +
        connection.escape(email),

        function(err, rows, fields) {
            if(rows[0].nb != 0) {
                callback();
            }
            else if(else_callback) {
                else_callback();
            }
        }
    )
}

so that you can call it like this:

//If the email hasn't a good format
if(email_not_good_format()) {
    //I do something
}
else {
    if_email_already_exists_in_mysql(email),function(){
        //I do something
    },
    // else
    function(){
        //I do something else
    }
)}

You can write async code to do pretty much anything regular code can do only instead of returning a value you pass in a callback. Remember:

return in synchronous code == passing in callbacks in asynchronous code.

The code structure must therefore be different but as I demonstrated above the logic you want to implement can be exactly the same.