you can use below plugin for authentication,
https://wordpress.org/plugins/jwt-authentication-for-wp-rest-api/
OR you need to implement auth by below methods,
https://developer.wordpress.org/rest-api/using-the-rest-api/authentication/
When you send request with username and password, you can get token as a response. Then you need to send this token with each request with header like below for the Authentication purpose,
syntax :
Authorization : Bearer< space >token
Example:
Authorization : Bearer eyJ0eXAiOiJKV1QiLCJhbGciOiJINiJ9.eyJpiOiJodHRwOlwvXC9hcHBzLm9wZW50ZXN0ZHJpdmUuY29tOjgwODBcL21hZ25pZmljZW50IiwiF0IjoxNDMjk1LCJuYmYiOjE0OTgxOTYyOTUsImV4cCI6MTQ5ODIwMzQ5NSwiZGF0YSI6eyJ1c2VyIjp7ImliMSJ9fX0.ngBJaXmtKAaBULSUtQZ7eHhqB8YSPjeHuI
