In my Prestashop I need not add some field in registration form. I tried in authentication.tpl and registration.tpl but not find any hint to add new field.Thanks in advance.
How to add field in registration form in prestashop 1.7?
You may start digging in classes/form/CustomerFormatter.php under getFormat() method. There is an array of fields for the registration form. I would guess you can override that method from your theme folder instead of editing it directly.
To add different fields, you need a module or to edit a lot of files to display and save the fields.
NOTE: these screenshots are from 1.6 but 1.7 country address are identical.
EDIT: Based on your screenshot, you don't have the standard registration option. Not sure it's available in 1.7. Anyway, the phone number field, in Prestashop is related to the addres, and not the customer. It would be easy to remove the other fields, but to add the phone number for the customer and not the address would be a little more tricky and would involve either create an address for that customer, or alter the customer table, class and forms.
One suggestion I can make is to translate the Company field to Phone number, and make it not optional. That would solve one problem.