New puppy

Hello everyone!

So I recently rescued a 6 month old terrier mix. He is a very sweet dog and he is doing pretty good at potty training. The issues I’m running into is his behavior with my current dog. I currently have a 3 year old Boston terrier. At first they got along pretty good, besides my new puppy playing a little rough. But the past couple of days I’ve noticed my rescue puppy snapping at my Boston over attention. Last night my puppy was laying on me, and my Boston came over to get pet and my puppy snapped at him. Then today, my puppy snapped at my boston again today and was growling over attention. I have been giving them equal attention as well. Is this normal behavior for a shelter puppy? If it is what is the best way to nip it in the butt? My puppy is pretty stubborn, so the redirecting and gentle training isn’t working out the best. I also don’t wanna put him in his cage for time out because I don’t want him to associate his cage with punishment. If anyone has some advice I’d really appreciate it. I really wanna see them become best buddies, because my Boston was best buddies with my last dog who passed away.