The right aproch is to create a new custom module.
Preference, extends, plugin this model as you prefer \Magento\Catalog\Ui\DataProvider\Product\Form\Modifier\AdvancedPricing::getTierPriceStructure
inserting your custom new field.
After that please create new custom table with db_schema.xml.
Than create a plugin after product save which handle the product save and customize this model (with Preference, extends, plugin) \Magento\Catalog\Model\Product\Attribute\Backend\TierPrice\SaveHandler
for retrive the custom value.
Cheers