My android phone instal app on it own I use Evercoss AT1A and I have problem with my phone.  It installs applications on its own, without my permissions. 

Can someone tell me how to fix it?  It doesn't update any applications, it installs new application,  that I don't know and don't want to install.
Some trojan/viruses do those kind of things, once they got the superuser privilege on your device they will auto install applications from playstore without any intervention from you, try to scan it with Malware bytes or Dr Web Antivirus to check if you are infected. I so far encountered 2 phones behaving same as what you described and found out it is infected. By the way those two phones are never rooted and all applications installed on it all came from google playstore.