Are the sites appearing in your Awesome bar bookmarked? If that is the case, it will still give bookmark suggestions even though your history is cleared. Clearing Location bar history offers some details into that.

Go to Options>Privacy>Location Bar>Select a suggestion ranging from Nothing to History&Bookmarks.

See also:

• https://support.mozilla.com/kb/Cannot+clear+Location+bar+history

Thanks. Sites appearing in awesome bar are not bookmarked. And when using "nothing to history&bookmarks" for location bar it only hides visited sites while using this ranging. But if I change location bar option back to using history and bookmarks it remembers also sites visited while it was tagged "nothing to history&bookmarks" and it wasn't suppose to remember those sites. And somehow clearing all history when closing firefox does not clear all of it.

The location bar setting is only for viewing and autocomplete purposes and doesn't influence the storing of visited sites or sites that you typed or pasted in the location bar.
You can only prevent that if you disable the history.

If older sites that you haven't visited recently show as history in the location bar then try to remove ll places files in the Firefox Profile Folder

• http://kb.mozillazine.org/Bookmarks_history_and_toolbar_buttons_not_working_-_Firefox
• https://support.mozilla.org/kb/Bookmarks+not+saved#w_fix-the-bookmarks-file

You can use this button to go to the Firefox profile folder:

• Help > Troubleshooting Information > Profile Directory: Open Containing Folder