I have a window that says searchdaemon will damage your computer. This file was downloaded on an unknown date. I did not down load nor can I find how to delete or transfer to trash. Apple directions don't help. How do I get rid of it?

That advisory is shown in this Apple support document:

Safely open apps on your Mac - Apple Support

You can do "Show in Finder to give to the location, then delete the file.

The file name suggests macOS intercepted an attempt to load adware, likely caught when you downloaded something else from an unscrupulous download hosting sites. Those sites make money by giving you free grief with the "free" download. You are always in danger when you use sites that claim to give you something free that you know costs money elsewhere.

The most common file types carrying hidden adware are fonts; screensavers; and ringtones.

Lizardtrail wrote:

Did not resolve the issue.

Likely adware. Download and run EtreCheck, then open a new reply here and then press the Additional Text button that looks like a printed page to get a text input box big enough to paste the hardware and software configuration report here, and paste and post that report here.

You’ll need to run that tool, share the generated report to the clipboard, and post the report here in the Additional Text box.