This version of Xcode isn’t supported in this version of macOS.

Which version of Xcode are you trying to install on macOS Sequoia 15 Beta ?

From macOS Sequoia 15 Beta Release Notes:

The macOS 15 SDK provides support to develop apps for Mac computers running Sequoia 15 beta. The SDK comes bundled with Xcode 16, available from the Mac App Store. For information on the compatibility requirements for Xcode 16, see Xcode 16 Release Notes.

Further, Xcode 16 beta requires a minimum of macOS 14.5.

Not the original poster - however did encounter this as well on my personal laptop so I'll be more specific:

Latest AppStore version of Xcode won't launch under MacOS sequoia. Only the beta.

This means it's hard to evaluate and continue working and submit apps while trying the beta if a user has only 1 laptop and is an active iOS / MacOS developer.

This annoyingly has been the case for the past three years; new major versions of macOS won't allow previous major versions of Xcode to launch.

But there's a workaround, you can either launch that Xcode from the command line:

❯ open /Applications/Xcode.15.4.0.15F31d.app/Contents/MacOS/Xcode 

Or via the Finder by right clicking on the Xcode, selecting 'Show Package Contents' and opening the binary executable directly (at the same path as above).

It doesn’t work on Monterey 12.7.5?i can’t download Xcode,it asks me to install mac os version 14 or higher.what’s the problem?

There is still a way to use your existing xcode. I have written a tutorial on that as well as made a video on that. You can search on Google for it, its written on codespeedy website.