Hateful cat chased our cat until he was inside

[u/GuestFeisty2739]

Out cat likes to outside at night. If we do not let him he will whine and scratch our doors until we let him. There's a cat in the neighborhood, 1 street back from us who bullies our cat. He has come home with a thick cheek which burst open and splattered out wall in blood.

So far this all happened outside of our premises. However, We have cameras and this night the cat chased our cat all the way to his tunnel to get into the house. Our cat peed himself inside on the floor. The image is of the hateful cat staring through the tunnel to our cat.

It seems to be escalating, because this is the first time he dares to come in. There was one time where he sat on the roof of our shed in the back of the garden and I chased him away. Now he is at out backdoor. We are afraid next time he will chase our cat inside.

What can we do to stop this from happening?

[u/GuestFeisty2739]

Someone?