I understand that you are looking for an American TV series about the alien Allen. However, no TV series fully conforms to this plot. However, there is an American drama called Alien Residents. Its hero is Allen, an alien.

The protagonist (alan tudyk) in Alien Residents first came to earth for a single mission. He should have put down the probe and returned immediately, but he was accidentally forced to stay on earth. Soon, aliens found that the barren hills and snow were almost a place of the world, and there was a doctor living alone.

If you are interested in this program, you can find it on many streaming media platforms, or search it in your local TV guide for more information. If you have any other questions about this project, I will be happy to help you.