Craft 3 Plugin: Unable to add a new method to EntryQuery
You know you don't add a new function to Crafts EntryQuery you create a custom Element type with a custom Query and add a function to that one. By the way you should probably fix your namespaces

use by\prefix\elements\db\BirthdateQuery;
use by\tariffsinfo\elements\BirthdateElement;


In order to use your function you'll have to do 

BirthdateElement::find()-&gt;birthdate('whatever');


To search for a custom field in an entries FieldLayout you just need to call the parameter by handle... So when you include a field into the layout with the handle birthday you can do

{% set entries = craft.entries.birthday('whatever').all() %}


When you want to search for your custom element type in your frontend you'll have to include a function to Twig like Craft does

/**
 * Returns a new EntryQuery instance.
 *
 * @param mixed $criteria
 * @return EntryQuery
 */
public function birthdays($criteria = null): BirthdateQuery
{
    $query = BirthdateElement::find();
    if ($criteria) {
        Craft::configure($query, $criteria);
    }

    return $query;
}


So you can access it via

{% set birthdates = craft.pluginName.birthdays.id(2).birthdate('whatever').all() %}