Not a lot of information to go on with your post, so I will try offering some basic steps to try.
First, ensure that your external SSD meets the following criteria:
- File System: macOS requires the drive to be formatted as APFS for macOS installations.
- Partition Scheme: The disk should use GUID Partition Map (GPT).
If it does already, then the next step would be to prepare this drive for the macOS installation.
- On your Mac, go to Applications > Utilities > Disk Utility.
- Select your external SSD in the left sidebar.
- Click Erase.
- Choose:
- APFS as the format.
- GUID Partition Map as the scheme.
- Click Erase to confirm.
Sometimes, the macOS installation file may be corrupted. Delete the existing Sonoma installer and redownload it from System Settings > Software Update or the Mac App Store.
Finally, try run the Installer, and choose the external SSD as the destination.