How to insert a record by clicking on the link using AJAX

If this is your request data for an AJAX POST:

data: {
    action: 'gs_order',
    nonce_data: ajax_vars.nonce,
    product_groups: $(this).data("pgid"),
    products: $(this).data("pid")
},

Then you access product_groups and products like this:

$data = [
    'product_groups' => $_POST['product_groups'],
    'products'       => $_POST['products'],
];

Just make sure you sanitize and escape the data as required. If they’re going to be IDs you can just use absint():

$data = [
    'product_groups' => absint( $_POST['product_groups'] ),
    'products'       => absint( $_POST['products'] ),
];

And to verify the nonce, use:

check_ajax_referer( 'gs_nonce', 'nonce_data' );

So all together:

function gs_ajax_callback()
{
    check_ajax_referer( 'gs_nonce', 'nonce_data' );

    $data = [
        'product_groups' => absint( $_POST['product_groups'] ),
        'products'       => absint( $_POST['products'] ),
    ];

    $order = new Group_Shop_Order();
    $order->create_order( 194, $data['products'], $data['product_groups'] );

    wp_die();
}

PS: I have no idea what Group_Shop_Order is, or how it works, so I can’t say whether the usage of $order->create_order() is correct. I’m just going of your code for that.

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