Cannot sign on to site. Says I need to update my macOS on my Mac. Did everything instructions said and My mac is updated and still cannot sign on to site.

Chase requires Safari 16 or later (if you use Safari).

To upgrade Safari to Safari 16 or a later version you would need to upgrade your Mac to macOS 11 or a later version.

If you can’t or don’t want to upgrade, you may want to use a 3rd party internet browser that supports running their current version on your Mac. One option is Chrome: https://www.google.com/chrome/

The model year of an iMac is available at Apple menu > About This Mac.

A late 2012 through late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. See: How to download and install macOS - Apple Support

A mid 2014 and late 2014 iMac can be upgraded to the latest version of Big Sur macOS 11 but no later. See: How to download and install macOS - Apple Support

A late 2015 iMac can be upgraded to the latest version of Monterey macOS 12 but no later. See: How to download and install macOS - Apple Support

A 2017 iMac can be upgraded to the latest version of Ventura macOS 13 but no later. See: How to download and install macOS - Apple Support  

A 2019 or later iMac can be upgraded to the current version of Sonoma macOS 14. See:How to upgrade to macOS Sonoma - Apple Support

This is clearly Chase Bank's problem to fix. They are the only major institution clinging to an old and outdated method of determining browser compliance. They need to stop doing that.

If you are motivated to do so direct their attention to this excerpt from Apple's Safari Developer Documentation (emphasis added):

Important

Use feature detection to enable or disable functionality instead of relying on the name or version of the browser in the User Agent string. Learn how to detect available features on MDN…

The passage regarding feature detection in that document uses even stronger language:

"... this is a terrible practice that should be discouraged at all costs."

Unfortunately, Chase's continued use of that terrible practice leaves you out in the cold until they realize the error of their ways and correct it.

The workaround for end users who are unable to update their Macs to a newer macOS version is to use a different browser.

Consider Brave:

https://brave.com/

Firefox is a distant second choice:

https://www.mozilla.org/en-US/firefox/new/

The bottom line is that there is nothing wrong with your Mac's version of Safari, but that bank is using an outdated and ill-conceived method of determining browser requirements.