Bitrix Framework

You can organize page navigation in AJAX-action by implementing in the method parameters \Bitrix\Main\UI\PageNavigation and return \Bitrix\Main\Engine\Response\DataType\Page.

Example:

use \Bitrix\Main\Engine\Response;
use \Bitrix\Main\UI\PageNavigation;

public function listChildrenAction(Folder $folder, PageNavigation $pageNavigation)
{
	$children = $folder->getChildren([
        'limit' => $pageNavigation->getLimit(),
        'offset' => $pageNavigation->getOffset(),
    ]);

	return new Response\DataType\Page('files', $children, function() use ($folder) {
		//lazy evaluation of total records as per filter		
		return $folder->countChildren(); 	
	});
}

To pass page number in JS API, take note of navigation.

BX.ajax.runAction('vendor:someController.listChildren', {
	data: {
		folderId: 12 
	},
	navigation: {
		page: 3
	}
});

For example, in case of REST, calculation of total records is always required, but for standard AJAX it's optional. More performance and convenient is to use a separate AJAX-action for getting total records as per specific filter.