goskm75f Did you install Google Play before or after Telegram? If you installed Google Play afterwards, then notifications won't work.
You can try clearing Telegram's storage, which would mean losing chats and settings and you'd have to log in again, so be sure to back up your data first. After clearing the storage and setting everything back up again, I'd expect notifications will work then.
To do that: long press Telegram's icon > app info, the circle with an i in it > Storage & cache > clear storage