If you have (two-factor authentication), then the password you should enter would actually be a PAT (Personal Access Token), in your settings, not your GitHub account password.
For me, after doing the token sign up using the Android studio UI in Preferences - Github also requested again username/password after doing git pull, what I did to solve it is to place my username and in password paste again the copied token
Steps
Go to github developer settings
Generate a new token with repo, gist, read:org privileges
Copy the token
Go to android studio preferences-github press the - sign if you have another account and press the + sign to add a new account
Go to the use token link
Paste your copied token
Now your account is added to the IDE, press apply and OK
Now do a git pull (if you already are in a repo)
If asking for username , place your github username
If asking for password, do not put your github password, instead paste again the token you created there and press enter
In the latest version of Android studio, click Use token and then Generate. Your browser will open the link and then click on Generate Token, copy the code and paste it on Android studio.
I was authenticated in Android Studio Arctic Fox (Latest Version) using a personal access token, but still, I was getting this error on August 14, 2021:
remote: Support for password authentication was removed on August 13, 2021. Please use a personal access token instead.
I generated a new access token on github.com, removed my GitHub account from Android Studio, and added the account again with the new access token. But still, it was showing the same error.
Reading other solutions on SO, I downloaded the GitHub CLI, and added my GitHub account in the windows command prompt with the access token successfully, and tried to push the repo from Android Studio again, which again failed.
Then following this article, I did the following in command line:
cd <project-directory>
git remote set-url origin https://<TOKEN>@github.com/<user_name>/<repo_name>.git
Pushed again from Android Studio. It worked finally!