Thank you, @yvan, for answer. Links you added are good.
But there are better documentation in source code comments. If you want to understand how it works you should look through files includes/ajax.inc and misc/ajax.js.
My problem was solved like this:

(function($) {
Drupal.behaviors.MyModule = {
    attach: function (context, settings) {
        
        // Overwrite beforeSubmit
        Drupal.ajax['some_element'].options.beforeSubmit = function (form_values, element, options) {
            // ... Some staff added to form_values
        }
        //Or you can overwrite beforeSubmit
        Drupal.ajax['some_element'].options.beforeSerialize = function (element, options) {
            
            // ... Some staff added to options.data
            // Also call parent function
            Drupal.ajax.prototype.beforeSerialize(element, options);
        }

                    //...

These functions are calling in jQuery Form Plugin.

Thank you, @yvan, for answer. Links you added are good.
But there are better documentation in source code comments. If you want to understand how it works you should look through files includes/ajax.inc and misc/ajax.js.
My problem was solved like this:

(function($) {
Drupal.behaviors.MyModule = {
    attach: function (context, settings) {
        
        // Overwrite beforeSubmit
        Drupal.ajax['some_element'].options.beforeSubmit = function (form_values, element, options) {
            // ... Some staff added to form_values
            // return false; // to prevent AJAX call if needed.
        }
        //Or you can overwrite beforeSubmit
        Drupal.ajax['some_element'].options.beforeSerialize = function (element, options) {
            
            // ... Some staff added to options.data
            // Also call parent function
            Drupal.ajax.prototype.beforeSerialize(element, options);
        }

                    //...

These functions are calling in jQuery Form Plugin.