Web App accessing data from private sheet

I am creating a web app, which requires fetching data from google sheet and writing data to that same google sheet. I can implement this if the sheet is public, I don't know how to do this for a private sheet (can be accessed by only those who has been given access). I am using the google apps script on the server-side (using doget and similar functions and then publishing the same as a web app) and using the fetch method on the client-side using javascript. Can I do this on a private sheet?