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I'm not entirely sure what the problem with the ftp.nsysu.edu.tw host is, but at least for packages.ros.org you don't appear to have the correct key imported.

Refer to #q325039 for instructions on how to fix that.

Then run a sudo apt update again.

I'm not entirely sure what the problem with the ftp.nsysu.edu.tw host is, but at least for packages.ros.org you don't appear to have the correct key imported.

Refer to #q325039 for instructions on how to fix that.

Then run a sudo apt update again.

I'm not entirely sure what the problem with the ftp.nsysu.edu.tw host is, but at least for packages.ros.org you don't appear to have the correct key imported.

Refer to #q325039 for instructions on how to fix that.

Then run a sudo apt update again.

Edit:

and try sudo apt update it still not works:

E: The repository 'http://ftp.nsysu.edu.tw/Ubuntu/ubuntu xenial Release' does not have a Release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.
E: The repository 'http://ftp.nsysu.edu.tw/Ubuntu/ubuntu xenial-updates Release' does not have a Release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.
E: The repository 'http://ftp.nsysu.edu.tw/Ubuntu/ubuntu xenial-backports Release' does not have a Release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.
E: The repository 'http://ftp.nsysu.edu.tw/Ubuntu/ubuntu xenial-security Release' does not have a Release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.

This is not a problem with the ROS package repositories, but with the ftp.nsysu.edu.tw host.

Do you know what ftp.nsysu.edu.tw is? Try using a different host.

In any case: the problem with the ROS package repositories seems to be fixed: you now have the correct key imported.