Can Quicken data file be kept on external ssd?

There is no problem having your Quicken data file on a mounted external drive. There are potential problems if this is a networked drive/NAS being accessed by multiple Macs. But if you're talking about moving the drive between different computers, that should be okay. But…

For maximum security, it's best to use a backup file or a compressed (.zip) copy of your data file when moving between computers. The reason is that the Quicken data file is a 'package' file which is actually a collection of files and folders inside a wrapper made to look like a single file. Because different Macs have different internal User ID numbers, it is possible for some of the contents of the package file to get its permissions fouled up -- the result of which can be you getting locked out of your data. We've seen these problems when people move a data file via Dropbox or iCloud between machines. In the case of an external drive where the file isn't being rewritten as its moved, I think you'll be okay. But to be absolutely safe, you can have your data file on the external drive, and just manually save a backup there each time you quit using Quicken. (Either Save a Backup from within Quicken, or just as easily, quit Quicken, click on the data file in the Finder and do File > Compress to create a .zip file; either way takes only a couple seconds.) When you sit down to use Quicken the next time, trash the .quicken file and double-click on the .backup or .zip file to launch Quicken from that file.