My cat is displaying very worrying territorial issue’s he is

My cat is displaying very worrying territorial issue’s he is attacking another cat and causing it to be hurt I am trying very hard to keep them separate but I’m wondering if anything can be done. He is neutered and has always been an outdoor cat
JA: I'll do all I can to help. When did you first notice this aggression?
Customer: We have a neighbour who insists even after being asked on several occasions to not feed the cats dreamies from her window persists doing this for probably the last 7-8 months and that is how long it has been going on before that my cat although out all the time was never in the garden now he spends all his time when out under her window to get the treats and fights with the other cat for dominance I am at my wits end I do not want to see either cat rehired or my cat have to be put to sleep
JA: Have you tried anything so far that helps the cat with his aggression?
Customer: what can I try I’m open to suggestions he is not aggressive at home
JA: And what's the cat's name and age?
Customer: his name is ***** ***** he is about 7 and a half
JA: Is there anything else the Vet should know about Leo?
Customer: not really indoors he is loving although I do have another male cat that he sometimes bullies but he has learnt to just stay away from him