I’m encountering issue in updating apple watch series 3. I received a message saying: an error occurred downloading the latest version of watchOS. I have tried many ways but failed.

Hello and welcome to Apple Support Communities, BoboYii!

I understand you're not able to update your Apple Watch. I'd be happy to provide information to help you address this.

Give the steps here a try: Update your Apple Watch

"If you need help updating

Try these steps:

1. Make sure that your Apple Watch connects to its charger. 
2. Restart your Apple Watch. Press and hold the side button until you see Power Off, then drag the slider. To turn your watch on again, press and hold the side button.
3. Restart your paired iPhone. Press and hold the Sleep/Wake button until the red slider appears, then drag the slider. To turn your iPhone on again, press and hold the Sleep/Wake button. 
4. Try to start the update again. 

If the update won't start, open the Apple Watch app on your iPhone, tap General > Usage > Software Update, then delete the update file. After you delete the file, try to download and install watchOS again."

Have a great day!