extending Wifi from ethernet connection with Time Capsule

You will need to perform a Hard Reset on the Time Capsule, as it will need to be reset back to factory default settings before it can be configured with the new settings that it needs to work with your existing modem/router.

The Hard Reset will not affect any of the data stored on the Time Capsule hard drive. However......if you have "upgraded" your Macs to Catalina, unfortunately a number of users have reported that their older backups are no longer visible.....since Apple has made a number of undocumented changes with Time Machine in the Catalina operating system.

Bottom line......we can't predict whether or not things will work or not with your old backups, but you should be able to start new backups from this point moving forward.

To perform the Hard Reset.......power up the Time Capsule (TC) for a few minutes......if it is not already on.

Hold in the reset button on the back of the TC for 7-8 seconds and release

Allow a full minute for the TC to restart to a slow blinking amber light status

On your Mac.....

Click on the WiFi menu item at the top of the Mac's screen

Look for a listing of New AirPort Base Station

Click directly on AirPort Time Capsule....or....it might read simply Time Capsule depending on the model of TC that you have

When you click on Time Capsule, that will start up the AirPort Utility setup "wizard" automatically. The wizard will take a few seconds to analyze the network and then display a screen that will look similar to the example below, except that you will see a Time Capsule pictured.

Wireless Network Name.......Type in the exact same wireless network name that your modem/router is now providing

Base Station Name.......Type in a device name that you want to call the Time Capsule. Example.......Time Capsule

Password......Type in the exact same password that the modem/router WiFi network is using

Verify......Type in the same password again to confirm

Click Next

The wizard will set up everything for you automatically. When you see the message of Setup Complete, click Done

And.....you are done with the setup

The Time Capsule is now providing extended WiFi coverage for your modem/router WiFi network.

If you are using Time Machine to back up the Mac, try to run a backup.

I have connected my Time Capsule to my non Apple router/modem by ethernet.

The Time Capsule can indeed provide more coverage for your existing network.....IF.....it is configured correctly.....AND.....the Time Capsule is located in the area where you need additional wireless coverage for your WiFi network.

Just to confirm......you have connected the Ethernet cable from one of the LAN <--> Ethernet ports on the modem/router......(there are usually 4 of them.....choose any one that you want)......to the WAN "O" port on the Time Capsule, correct?

And, you understand that the Time Capsule must remain connected to your modem/router at all times with the Ethernet cable connection, correct?

The next question would be whether or not you have performed a Hard Reset on the Time Capsule.....because that would be required.....before.....you can set up the Time Capsule to provide additional wireless signal coverage.

Thanks go to the AirPort Utility setup "wizard" which has the "brains" to automatically apply the correct settings for your setup.