How I can get rid off search alpha from my research?

First, ensure you have a reliable backup of your Mac, in case something should go wrong with continued troubleshooting. To learn how to do that, please read Back up your Mac with Time Machine.

• A backup is a fundamental prerequisite regardless of whatever method you may choose uninstall adware, and would apply even if your Mac were running perfectly well. Do not overlook this fundamental requirement. It's important.

Next: This step will prevent the scam products from loading so that they can be removed while they are inactive. Restart in "Safe Mode", and log in: How to use safe mode on your Mac - Apple Support. Starting in Safe Mode takes longer than usual so let it finish. The rogue processes affecting that Mac are inoperative in "Safe Mode".

The following files and / or folders need to be deleted while using your Mac in "Safe Mode":

First screenshot:

Nothing needs to be deleted from the folder in the other two screenshots, but please read my comments regarding "Anydesk" later.

Drag those selections of files to the Trash. You may be asked to authenticate. Confirm they are no longer present in that folder. Leave all the others alone for now.

Next: open Safari and select the Safari menu > Preferences (or Settings) > Extensions. If you see any Safari Extensions that you do not recognize or understand, simply click the Uninstall button and they will be gone. No Safari Extensions are required for normal operation. Then, select the General pane and review your Homepage selection. Then, select the Search pane and confirm your desired Search Engine. Repeat those equivalent actions for any other browser you may use (Brave, Firefox, or Opera for example).

• Specifically for Google Chrome: If you use it, you will also need to reset the Chrome product to its default settings. To learn how to do that read https://support.google.com/chrome/answer/3296214?hl=en

There may also be adware-associated app icons in your Mac's Applications folder. Open it and examine its contents. Any unwanted or mysterious app icons should be obvious to you, but again please don't remove anything if you are uncertain—ask first. Identify any suspicious apps by name, or post another screenshot.

Next: In an abundance of caution, examine System Preferences (or Settings) > Extensions. Determine if there are any System Extensions that may have been installed without your knowledge. Ask if you're uncertain.

Remaining in System Preferences, check for the presence of any Profiles. Profiles are installed by organizations with a need to manage Macs deployed in institutional corporate or educational environments (for example), but have also been exploited by adware creators and similar malcontents. If any Profiles are installed on your Mac an icon like this will appear in System Preferences:

If you see that icon in System Preferences, select it. To remove a Profile, select it, then click the [—] (minus) button and authenticate.

Remaining in System Preferences, open Users & Groups. Select your User Account's Login Items. You may or may not find those Applications in its list. If you do, select them then click the [—] (minus) button to remove them from Login Items.

You can then restart your Mac and log in as usual. Evaluate its operation and ensure everything is working as you expect it should.

Next: Regarding the "Anydesk" product, the following Discussion may be of interest to you: AnyDesk installed by scammer - Apple Community. If you contacted any number of unscrupulous entities in an attempt to rid that Mac of the problematic "Search Alpha" redirect (or any other problem) you may have invited additional troubles. If you are 100% certain that you installed the "Anydesk" product intentionally and are just as certain that you need it, then please disregard this comment as irrelevant and unrelated to the problem at hand.

Next: if you want to eradicate all remaining adware remnants post a screenshot of the following folder, in the same manner as you did earlier:

~/Library/Application Support

It is normal for that folder to contain many items, but anything associated with the above adware may contain identical names. If you find a folder or folders bearing those names, drag those folders to the Trash. Without the files you already removed or the reintroduction of similar malware, they can do nothing but occupy space. These can be removed if you wish, but again don't remove anything if you are uncertain.

Finally: If any of the above actions result in abnormal operation or if something else stops working, the easiest way to recover would be to restore the Time Machine backup you created as a prerequisite, so the importance of that fundamental step cannot be overemphasized.

jetlira89 as Mr etresoft wrote posting screenshots with complete, readable file names would help. With the understanding that we may be working with incomplete information, please follow the instructions in my next post. They are conservative in nature and will only ask you to remove specific files that are known to be problematic.

If the problem is resolved after following these instructions, great! If not, or if the problems arise in the future, please post three brand new screenshots showing the information described in Removing "Search Marquis" / "Search Baron" / etc on your own - Apple Community.

Aside: In lieu of of what follows below you may also consider using EtreCheck, which will reveal complete details regarding those files as part of its comprehensive report. For instructions regarding its use please read How to use the Add Text Feature When Posting Large Amounts of Text, i.e. an Etrecheck Report - Apple Community. I can work with it just as easily, so decide what's best for you.

Uninstall your malware. You seem to have quite a bit of it. Can't tell much from your truncated screenshots however.