How to Filter WordPress Posts by Category Using AJAX, without using any plugin

jQuery(document).ready(function ($) {
    // Fetch all worksheets by default when the page loads
    fetchWorksheets();

    // Trigger AJAX request when a grade filter is selected
    $('.grade-filter').on('change', function () {
        var taxonomy = $(this).data('taxonomy'); // e.g., 'worksheet-grad'
        var term = $(this).val(); // Selected term slug
        fetchWorksheets(taxonomy, term);
    });

    // Function to fetch worksheets
    function fetchWorksheets(taxonomy = '', term = '') {
        $.ajax({
            url: ajax_object.ajax_url,
            type: 'POST',
            data: {
                action: 'fetch_worksheets',
                nonce: ajax_object.nonce,
                taxonomy: taxonomy,
                term: term,
            },
            beforeSend: function () {
                $('.worksheet-container').html('<p>Loading...</p>');
            },
            success: function (response) {
                if (response.success) {
                    $('.worksheet-container').html(response.data.html);
                } else {
                    $('.worksheet-container').html('<p>' + response.data.message + '</p>');
                }
            },
            error: function () {
                $('.worksheet-container').html('<p>An error occurred. Please try again.</p>');
            },
        });
    }




});

// Register AJAX action for logged-in users (you can add for non-logged-in users too)
add_action('wp_ajax_fetch_worksheets', 'fetch_worksheets');
add_action('wp_ajax_nopriv_fetch_worksheets', 'fetch_worksheets');

function fetch_worksheets() {
    // Verify nonce for security
    if (!isset($_POST['nonce']) || !wp_verify_nonce($_POST['nonce'], 'ajax_nonce')) {
        wp_send_json_error(array('message' => 'Nonce verification failed.'));
        wp_die();
    }

    // Get taxonomy and term from the AJAX request
    $taxonomy = isset($_POST['taxonomy']) ? sanitize_text_field($_POST['taxonomy']) : '';
    $term = isset($_POST['term']) ? sanitize_text_field($_POST['term']) : '';

    // Default query arguments
    $args = array(
        'post_type'      => 'worksheet',
        'posts_per_page' => -1, // Fetch all posts
    );

    // If a specific term is selected, modify the query
    if (!empty($taxonomy) && !empty($term)) {
        $args['tax_query'] = array(
            array(
                'taxonomy' => $taxonomy,
                'field'    => 'slug',
                'terms'    => $term, // Fetch posts of the selected term
            ),
        );
    }

    // Run WP_Query to fetch posts
    $query = new WP_Query($args);

    // Check if any posts were found
    if ($query->have_posts()) {
        $html = '';
        while ($query->have_posts()) {
            $query->the_post();
            // Output the post HTML
            $html .= '<div class="card">';
            $html .= '<h3>' . get_the_title() . '</h3>';
            $html .= '<div class="worksheet-excerpt">' . get_the_excerpt() . '</div>';
            $html .= '</div>';
        }
        wp_send_json_success(array('html' => $html));
    } else {
        wp_send_json_error(array('message' => 'No worksheets found.'));
    }

    wp_die(); // Always terminate the request properly
}

function enqueue_custom_scripts() {
    wp_enqueue_script('custom-ajax', get_template_directory_uri() . '/js/custom-ajax.js', array('jquery'), null, true);

    // Localize script to pass ajax_url and nonce to JS
    wp_localize_script('custom-ajax', 'ajax_object', array(
        'ajax_url' => admin_url('admin-ajax.php'),
        'nonce'    => wp_create_nonce('ajax_nonce'),
    ));
}
add_action('wp_enqueue_scripts', 'enqueue_custom_scripts');

 <div class="grade">
            <h2 class="filter-heading">GRADE</h2>
            <ul>
                <li>
                <input type="radio" id="1st" name="radio" class="grade-filter" data-taxonomy="worksheet-grad" value="1st-grade" />
                <label for="1st" class="font">1st Grade</label>
                </li>
                <li>
                <input type="radio" id="2nd" name="radio" class="grade-filter" data-taxonomy="worksheet-grad" value="2nd-grade" />
                <label for="2nd" class="font">2nd Grade</label>
                </li>
            </ul>
            </div>