Wifi automation

For couple weeks I'm trying to find a way automaticly turn on wifi for like a half min, while the screen is off, and then turn it back off. You know, just sync quickly with social media, emails, etc, but still not connect all the time, to save battery. But I can not do it... I tried numerous app from the Play(even bought Tasker...), but non off it works, when I turn off my screen its just wont connect to wifi no matter what. Maybe its related to Stamina mode, but I'm not sure.
Any suggestion how to resolve this?