Store unique Key to verify legit APK

Question

I want to publish an Android App.
My Question is how to check if an App is signed with my Certificate?

To be more specific:
I have an app that always needs an internet connection in order to do some
Actions.
It connects to a database where I can send and receive Data.
However my problem is that I don't know how to get some sort of
certificate/key that is only unique if the app is has not been tampered with (apktool, etc).

So what I want to do is:
- App is connecting to database and sends key as String
- database checks if key is alright
- App can proceed if key is alright otherwise try again screen

What I need to know:
- Is there a key that can change if apk has been tampered with
- How to get that key/certificate as string
- Is that key same for all Apks from Google Play

Thank you