Hello Rostyslav Sulym,
You can add filed in search view by adding your field in new view which must be inherited from the existing search view. 
<record id="sale_order_view_search_inherit_quotation" model="ir.ui.view">
            <field name="name">sale.order.search.inherit.quotation</field>
            <field name="model">sale.order</field>
            <field name="mode">primary</field>
            <field name="inherit_id" ref="sale.view_sales_order_filter"/>
            <field name="arch" type="xml">
                <xpath expr="//filter[@name='my_sale_orders_filter']" position="after">
                       <field name="your_field_name" />
                       <field name="your_field_name" />
                        <separator />
                       <field name="your_field_name" />
                </xpath>
            </field>
        </record>