Hi

Create a custom module and inherit the res.partner model

Python :

from odoo import fields, models

class ResPartner(models.Model):
    _inherit = 'res.partner'  # Inherit the res.partner model

product_id = fields.Many2one('product.product', string='Product')

    product_serial_number = fields.Char(string='Product Serial Number', related='product_id.your required_field)

<!-- res_partner_views.xml -->

<odoo>
<record id="view_res_partner_form_inherit" model="ir.ui.view">
<field name="name">res.partner.form.inherit</field>
<field name="model">res.partner</field>
        <field name="inherit_id" ref="base.view_partner_form"/>
        <field name="arch" type="xml">
            <field name="email" position="after">

                 <field name="product_id"/>
                <field name="product_serial_number"/>
            </field>
        </field>
    </record>
</odoo>

Once you choose a product the related field will be displayed.

Hope it helps