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First fix the basics: go to Settings > Date and time and turn on Automatic date and time, because a wrong clock breaks Google's secure connection on old Android. Then, because modern Google won't accept your normal password in Android 4.1.2's built-in account manager, turn on 2-Step Verification for your Google account and generate an app password at myaccount.google.com/apppasswords on a computer. Add the account via Settings > Accounts > Add account > Google and enter that 16-character app password instead of your usual one. See how others solved this on Reddit

On Android 4.1.2 the built-in account manager uses an old, insecure login method that Google now refuses, so your real password gets rejected even when it's right — especially once 2-Step Verification is on. The fix is to enable 2-Step Verification and generate a dedicated app password at myaccount.google.com/apppasswords, then enter that code in Settings > Accounts > Add account > Google. The device will sign in and sync normally afterward. See how others solved this on Reddit

On Android 4.1.2 this error is usually a wrong system clock or the old login method being blocked, not a network fault. Set Settings > Date and time to Automatic, confirm Wi-Fi actually reaches the internet (open a web page in the browser), then retry adding the account in Settings > Accounts > Add account > Google using an app password from myaccount.google.com/apppasswords rather than your regular Google password. See how others solved this on Reddit

Once the account is added with an app password, go to Settings > Accounts > Google, tap your account address, and turn on the toggles for Contacts, Gmail and Calendar, then open the menu and choose Sync now. If sync still hangs, remove the account and re-add it with a freshly generated app password, since Google's servers reject the old cached credentials from a previous attempt. See how others solved this on Reddit