ex keeps asking for my apple id

Little to none.

They can't access your iPhone without knowing the password.

They can't install any software without the password.

I don't think you need to be worried.

You can also add 2 Factor Authentication to your account for more security. If the attempts continue, you might want to consider a name change.

Link to contact Apple Support in the article.

Apple ID has been compromised.      *

Security and your Apple ID.   *

Device and Data Access when Personal Safety is At Risk    -

Checklist: If you want to see if anyone else has access to your device or accounts  *

 Apple ID Password Change.  -

Note the restrictions in the article.

Apple ID Name Change.  * 

Make sure you turn of Find My Phone before signing out of the old ID. Once signed out and Find My Phone is off, then sign in with the new ID, then turn Find My Phone back on.

 What to do after you change your Apple ID or password - Apple Support  *  I suggest doing this before you change your Apple ID or password.

Apple ID -Two-factor authentication   *

Two Factor Authentification availability.   *

2 Factor Authentication - How to generate a recovery key.  *

Apple ID - Using app-specific passwords.   *

Apple ID - Two Step Verifications FAQ    *

I don't believe this person can do anything to your account without being logged in. However, here is a guide with steps that you may find helpful.

If you think your Apple ID has been compromised - Apple Support