How to Implement Category.php page title in wordpress custom template?

Your code is fine, the only problem here is a syntax error. Always remember to remove any spaces between the opening and closing tags – otherwise your code will fail.

Example:

<h2>
    <a href="#" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>">
        <?php the_title(); ?>
    </a>
</h2>

Make sure to read the WordPress Codex about the_title_attribute() to understand better on how to customize this function: https://codex.wordpress.org/Function_Reference/the_title_attribute