Based on my research, the best app for downloading TV series without any subscription or membership fees is Google Play Movies & TV. With this app, you can rent or purchase TV shows and movies and download them for offline viewing. The app is available on Android, iOS, and Chrome OS devices, and it allows you to download videos in standard or high definition.
Another option is Netflix, which offers a download feature for offline viewing. However, this feature is only available for select TV shows and movies, and it requires a subscription to the service.
Other streaming services that allow downloads for offline viewing include Amazon Prime Video, Hulu, and YouTube. However, these services may require a subscription or membership fees.
It's important to note that downloading TV shows and movies from unauthorized sources is illegal and can result in legal consequences. It's always best to use legitimate streaming services to access your favorite content.