Hello Christos M.,
Thanks for using the Apple Support Communities.
I see that you are having an issue trying to watch purchased TV shows on your iPad TV app. It's prompting you to purchase these shows again, but you're able to watch these fine on your Apple TV. I can understand wanting to watch these shows on all of your devices without any issues. I'm happy to help you try and get this resolved.
I suggest trying to re-download these purchases using the steps in support article:
Download your past purchases
, specifically:
You can only redownload a movie or TV show that you bought from the iTunes Store. Rented movies are not available for redownload.
You can redownload movies and TV shows on your iPhone or iPod touch, iPad, Mac, or PC. You can watch previously purchased movies or TV shows on your Apple TV, but they don't download to the device.
On an iPhone, iPad, or iPod touch, you can redownload movies and TV shows in the TV app (U.S. only; iOS 10.2 or later) or the Videos app. You can also redownload items from the iTunes Store app.
TV app
In the TV app, you can only redownload items that you bought from the iTunes Store.
- Open the TV app.
- From the menu at the bottom of the screen, tap Library.
- Depending on what you want to download, tap Movies or TV Shows.
- Find the movie or TV show that you want to redownload, then tap it.
- Tap . The video downloads to your device.
Videos app
- Tap Settings > Videos and make sure Show iTunes Purchases is on.
- Close Settings, then open the Videos app.
- Depending on what you want to download, tap Movies or TV Shows at the bottom of the screen.
- Find the movie or TV show that you want to redownload, then tap it.
- Tap . The video downloads to your device.
iTunes Store
If you can't find an item in the TV app or Videos app, download it from the iTunes Store app:
- iPhone or iPod touch: Open the iTunes Store app and tap More > Purchased.
iPad: Open the iTunes Store app and tap Purchased.
- Depending on what you want to download, tap Movies or TV Shows.
- Find the movie or TV show that you want to redownload, then tap it.
- Tap . The video downloads to your device.
Let me know if this helps, or if you have any questions.
All the best.