I have a problem log in to my macbook due to forgotten password. I have tried everything with no success. The message appeared is cannot connect to the apple ID server. Any advise for this issues please?

If you what to change the Computer Password or Apple ID Password If your Apple ID is locked or disabled

Reset Computer Password 

Intel Computer

1 - Restart computer and immediately hold Command + r keys

2 - Top Tool Bar >> Utilities >> Terminal

3 - Type resetpassword as one word and no spaces

4 - Press Return key

5 - Follow the prompts and remember the New Password

Apple Silicon M1 Computer 

1 - Choose Apple menu > > Shut Down.

2 - Press and hold the power button on your Mac until you see “Loading startup options.”

3 - Click Options, then click Continue. 

4 - Top Tool Bar >> Utilities >> Terminal

5 - Type resetpassword as one word and no spaces

6 - Press Return key

7 - Follow the prompts and remember the New Password

The detailed method to Change Computer Password does not require an Internet Connection

To change Apple ID Password Does Require an Internet Connection.

The Two Passwords are independent form one another and for Totally Different Purposes.