Firstly we create a custom widget field end of the each widgets control form.

if ( ! function_exists( 'wpdocs_display_custom_field_in_widget_form' ) ) {

    add_action( 'in_widget_form', 'wpdocs_display_custom_field_in_widget_form', 10, 3 );

    /**
     * Append custom field end of the widgets control form
     * Fires at the end of the widget control form.
     */
    function wpdocs_display_custom_field_in_widget_form( $widget, $return, $instance ) {
        $column = isset( $instance['column'] ) ? $instance['column'] : '';

        ob_start(); 
        ?>

        <p>
            <label for="<?php echo esc_attr( $widget->get_field_id( 'itclan_bs_grid_class' ) ) ?>"><?php _e( 'Column Label', 'text_domain' ) ?>
                <input class="widefat" value="<?php echo esc_attr( $column ) ?>" id="<?php echo esc_attr( $widget->get_field_id( 'column' ) ) ?>" name="<?php echo esc_attr( $widget->get_field_name( 'column' ) ) ?>" type="text" />
                <small><?php _e( 'Some additional description.', 'text_domain' ) ?></small>
            </label>
        </p>

        <?php 
        echo ob_get_clean();
    }
}

Now, we filter widget’s settings before saving. It will save our custom field column data.

if ( ! function_exists( 'wpdocs_update_custom_field_in_widget_form' ) ) {

    add_action( 'widget_update_callback', 'wpdocs_update_custom_field_in_widget_form', 10, 2 );

    /**
     * Update widget fields
     * Filters a widget’s settings before saving.
     */
    function wpdocs_update_custom_field_in_widget_form( $instance, $new_instance ) {
        $instance['column'] = !empty( $new_instance['column'] ) ? $new_instance['column'] : '';
        return $instance;
    }
}

Finally, filter sidebar params for frontend. It will add class to before_widget from column field

if ( ! function_exists( 'wpdocs_filter_dynamic_sidebar_params' ) ) {

    add_action( 'dynamic_sidebar_params', 'wpdocs_filter_dynamic_sidebar_params' );

    /**
     * Update widget fields
     * Filters the parameters passed to a widget’s display callback.
     */
    function wpdocs_filter_dynamic_sidebar_params( $params ) {
        global $wp_registered_widgets;
        $widget_id        = $params[0]['widget_id'];
        $widget_obj       = $wp_registered_widgets[ $widget_id ];
        $widget_opt       = get_option( $widget_obj['callback'][0]->option_name );
        $widget_num       = $widget_obj['params'][0]['number'];
        $grid_class       = isset( $widget_opt[ $widget_num ]['column'] ) ? $widget_opt[ $widget_num ]['column'] : '';

        if ( preg_match( '/class="/', $params[0]['before_widget'] ) && $grid_class ) {
            $params[0]['before_widget'] = preg_replace( '/class="/', "class=\"{$grid_class} ", $params[0]['before_widget'], 1 );
        }

        return $params;
    }
}