I believe the only Arris modems that have an “onboard” battery backup are the phone modems, such as the following  https://www.rogers.com/support/home-phone/reset-the-battery-for-the-arris-tm402g-p-modem.

Are you looking for a backup battery  power supply, or UPS? If so, the modem AC cord plugs directly in to the UPS. You pick the size/capacity based on how long you need the modem to function when the main power is out. Here’s an example of such a unit. https://www.amazon.com/APC-Battery-Protector-BackUPS-BX1500M/dp/B06VY6FXMM/ref=sr_1_1_sspa?crid=32DV8Q1VMIFYB&keywords=UPS&qid=1694271500&sprefix=ups%2Caps%2C134&sr=8-1-spons&ufe=app_do%3Aamzn1.fos.18ed3cb5-28d5-4975-8bc7-93deae8f9840&sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&th=1

Thank you this is very helpful

Yes I need a UPS. Since most of them have a 6ft cable and I need 8ft, is it recommended to plug an extension on the outlet and plug the UPS on the extension?

I don’t think enough current is involved that it will matter whether the extension is on the UPS or the Modem. Just use a quality extension.

Thank you! I appreciate your help!