Odd!
Netgear make routers and I can think of no reason why your router should suddenly ask you for a password when you use a particular browser. However I can think of every reason why MALWARE on your computer could try to trick you into giving away your passwords!
Try downloading, installing and running the free version of Malwarebytes Anti-Malware:
https://www.malwarebytes.org/free/
Notes:
1. When installing it, take care to deselect the option to take a free trial of the full 'PRO' version ;
2. When running it, use the 'Quick scan' option ;
3. Don't be surprised if that so-called 'quick' scan takes over half an hour to run ;
4. When it's finished, click the to view the results. Ensure that there's a tick against everything found and then click again to get rid of it.