I have Apple TV 3 for 3 months when i go to watch a ty show only lets me watch the first episodes of shows

Most shows offer some episodes without a subscription, so it seems you haven't initiated the subscription (with 3 month trial for qualifying new purchase). See below on how to claim the offer.

1. Turn on your new Apple device and sign in with your Apple ID.
2. Open the Apple TV app. Make sure your device is running the latest version of iOS, iPadOS, tvOS, or macOS.
3. The offer should be presented immediately after launching the app. If not, go to the  Apple TV+ tabwhere you'll see the offer.
4. Tap Enjoy 3 Months Free.

That show would have the first episode available without subscription so as I said if you can't view more then it seems you didn't actually subscribe. You can go into your Apple ID to verify all current subscriptions. The steps provided above are how to claim the 3 month offer, you can also start regular subscriptions (with 7 day trial) from the TV app. If you are still having issues then contact Apple support.