Is this your first login with Fusion 360 or previously was Fusion 360 working. Generally this error/warning shows up when there are network configuration issue. Is this a home network or a work network with a proxy server and/or firewalls?
Generally speaking the suggestions in this link are the one to follow.
https://knowledge.autodesk.com/support/a360/troubleshooting/caas/sfdcarticles/sfdcarticles/Network-C...
It highlights what domains and ports Fusion will need to utilize. If this is a work network, you may need to share this information with the network administrator.
If you can look for application log files and attach them to your reply, we may be able to locate more specific error messages. If you can attach any log files you can find to the next reply I will be happy to look through them.
https://knowledge.autodesk.com/support/fusion-360/troubleshooting/caas/sfdcarticles/sfdcarticles/How...
It may also be helpful to try this diagnostic procedure if you haven't done so yet. There could be a background application interferring with the network communication.
https://knowledge.autodesk.com/support/fusion-360/troubleshooting/caas/sfdcarticles/sfdcarticles/Dia...
I hope this helps. Please let me know if you have any questions.
Thanks,
Nathan Chandler
Principal Specialist