I have a 3 month old terrier I just adopted and I must say he's pretty sharp. However when it comes to potty training it's a little complicated for him. He can easily let me know if he needs to go potty by barking once and jumping (he's usually chill). If I pick him up and take him outside... he knows to go into his routine to find his previous spot... uses it... and runs back in the house into his cage. But if I open the cage and let him go for himself... he finds a spot in the house... instead of walking to the door. Is there any possible way to fix the hole in his potty routine?

Why do you pick him up and take him outside ? Maybe this is the hang up; or use a leash and take him from his cage to the door. But how much time is he spending in the cage?

I agree with Tickle. It sounds like you've trained him that he needs to be picked up and carried outside to potty. Dogs only learn what we teach them. He's learned that if you don't pick him up, he can't potty outside, so he has to find somewhere else to potty.

You're going to have to change what you taught him. No more picking him up to potty outside. Lead him outside, lots of praise when he potties. Lots and lots of praise if he asks to go outside. This may take some time. He's going to have to learn something completely different than what he's already been taught.