First:
Cats wander, the laws accept that. Cats will cross property lines. You can call Animal Control and ask them to trap a feral cat or other animal.
The cat may like you. You may not recognize this, or understand why, but cats sometimes like people for no obvious reason. If it's scratching at your door, it may well be scent-marking; it may also need its claws trimmed and have no other good scratching post. Or it may just want your attention.
Second:
If you want the cat to recognize you as a possible intelligent life form -- always wise -- use the so-called 'cat kiss" -- when you notice a cat, look to the left, show it one side of your face for a few seconds. Then look smoothly _past_ the cat, without eye contact, and show it the other side of your face for a few seconds. Then, slowly, turn your face in the direction of the cat until you make eye contact, and close your eyes for a second or two. Then ignore the cat.
The cat will almost always make exactly the same series of moves -- it says "I see you, and I am not fixated on you so I am not going to attack." And likely enough it will come over to see if you want to make friends -- if you do it will start to respect you and your property.
Third:
Cats mark with their chins. If you want the cat to leave your property alone, scratch under her chin, then rub your fingers along the margins of the yard, doors, steps, plants. The cat will not stay away -- but it will recognize anything so marked as not to be damaged.
Fourth:
Why does the cat come into your yard? Garden? Sandbox? Space the cat finds clean, fresh, unmarked by other cats and so fits exactly the kind of spot it by nature looks for?
If so, make ONE spot -- preferably next to the neighbor's property -- fit the need. The cat will go there, by preference.
Fifth:
Do you stare at the cat? If so, this is monkey curiousity, but feline challenge. Combined with any attack, it will mark you for permanent attention.
Cats always focus in on people who stare or otherwise are nervous about them and call attention to the interaction.
Does the idea of doing something other than attacking the animal seem unattractive to you? Consider: if you want a war, attack a cat. No other common city animal except crows will so readily learn that you are to be attacked, and they are not as able as humans to back down and make peace. Cats don't surrender even to one another, let alone to mere primates.
They do, however, coexist very well indeed. As I said, the cat may like you.
Sixth:
"The man who carries a cat by the tail learns something that can be learned in no other way." -- Mark Twain.
Getting Started: Clicker Training for Cats
By Karen Pryor (Sunshine Books, Inc., 2001; $12.95)
Think you can't train a cat? With some patience, clicker-training expert Pryor believes that you can persuade your feline friend to learn behaviors like coming when called, staying off the dinner table and even performing tricks. Her method is based on rewards like food and attention - not punishment - so cats actually enjoy learning. Pryor writes with such clarity that beginners and seasoned cat people alike can easily follow along.