I want to add a filter on this dropdown.

The filter is a dropdown or select with options is a dynamic data, that is load form model

UI of filter maybe the same Add Customer Filter or image below:

How can I do that?

Now, my code:

<?xml version="1.0" encoding="UTF-8" ?>

<odoo>
    <record id="view_task_search_form_inherit" model="ir.ui.view">
        <field name="name">project.task.search.form.inherit</field>
        <field name="model">project.task</field>
        <field name="inherit_id" ref="project.view_task_search_form" />
        <field name="type">search</field>
        <field name="arch" type="xml">
            <xpath expr="//filter[@name='my_tasks']" position="replace">
                ...
            </xpath>
        </field>
    </record>
</odoo>