Greetings Diemydarling,
As per the pop-up, when you tap on ‘Verify Student Eligibility’ it should redirect you to the UNiDAYS site where you’ll be asked some questions and your eligibility will be verified.
Here’s more about the process - Get an Apple Music student subscription
How to reverify your student status
Near the end of each year that you have an Apple Music student subscription, you'll see a message that asks you to verify your student status in the Apple Music app or iTunes. You can also verify your student status at any time in the Settings app on your iPhone, iPad, or iPod touch.
In Settings on your iPhone, iPad, or iPod touch
1. Go to Settings > [your name], then tap Subscriptions.
2. Tap Apple Music Membership.
3. Tap "Verify your student status." You'll be redirected to the UNiDAYS website.
4. Follow the prompts to verify your eligibility. If the verification is successful, you'll automatically return to Apple Music and continue your Apple Music student subscription.
Thanks.