Type about:addons<enter> in the address bar to open your Add-ons Manager. Hot key; (<Control> [Mac=<Command>] <Shift> A)

In the Add-ons Manager, on the left, select Extensions. Remove “ yandex “ Anything.

Also look for SafeSearch, SearchAssist Incognito, FileConverter Addon, SearchLock, DiscreteSearch, WebSearch, Findwide Search Engine

Now do the same in the computer’s Programs Folder.

Windows: Start > Control Panel > Uninstall Programs. Mac: Open the Applications folder. Linux: Check your user manual.

Firefox from www.mozilla.org/firefox/all/ and internal Firefox updates do not come with any toolbars.

The Russian locale of Firefox does come with Yandex as the default search engine in the Search Bar and can be changed. https://support.mozilla.org/en-US/kb/add-or-remove-search-engine-firefox

https://blog.mozilla.org/blog/2017/11/14/firefox-features-google-as-default-search-provider-in-the-u-s-canada-hong-kong-and-taiwan/ https://blog.mozilla.org/blog/2014/11/19/promoting-choice-and-innovation-on-the-web/

I do not have any Yandex in the Addons nor in the computer program files, Fred.

@James, I took my Firefox from "https://www.mozilla.org/fr/firefox/", but looking at the first link you provide, I do not have the same look and feel (I can not find the magnifier for exampe ... with available search engines ?!?)

My version is Firefox Quantum, 58.0.2 (64 bits) ... is it correct ?

Still the Yandex toolbar is there.

P.S. I made a fresh installation and as you can see problem is still there :

The area that is circled in the first screenshot looks like 3 bookmarks on the Bookmarks Toolbar, with the Most Visited "gear" icon third from the left.

Plus I have yet to see a "toolbar" which was added to Firefox Quantum. I think that add-on toolbars are forbidden now. Many complaints over the last two months since Firefox 57 Quantum was released from users who had been using an extension that used to have a "toolbar" and the WE version of the extension has a flimsy version of a pseudo replacement for what used to be a fully fledged "toolbar".

Hide the toolbar or delete those bookmarks that appear in the Bookmarks Toolbar folder to verify what I have explained.

The-edmeister is right : those are bookmarks.

The first one is 'Yandex' and the second one is 'Mail' (also in Russian).

Would you give this a try :

Type in the address bar 'about:support' (without the apostrophes)

Then scroll down to 'Places Database' => 'Verify Integrity'

(Edited grammatical error)

I finally had to reinstall the computer to solve some other issues. So Issue with Mozilla is also now gone.

That was very good work. Well done. Please flag your last post as Solved Problem so others will know.

cdelecole said

I finally had to reinstall the computer to solve some other issues. So Issue with Mozilla is also now gone.

Probably a dumb question, but what exactly did you reinstall  ?

You mentioned earlier :

"I made a fresh installation and as you can see problem is still there "

Initially I have re-installed Mozilla, but issue (toolbar) was still there. I considered it was a virus / malwaere, as even deleting all I found in the windows registry concerning Yandex didn't solve the issue

So finally I have completely reinstalled my computer (windows ...)

cdelecole said

Initially I have re-installed Mozilla, but issue (toolbar) was still there. I considered it was a virus / malwaere, as even deleting all I found in the windows registry concerning Yandex didn't solve the issue So finally I have completely reinstalled my computer (windows ...)

So you did this :

https://support.microsoft.com/en-us/help/4000735/windows-10-reinstall

Only asking, because it may be helpful to others, with the same problem.