Hey, is the hat on this shadow person yellow?
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Why would you sooner believe someone who has perception disabilities? Do you think that they are more open to paranormal activity than those who do not have those types of problems?
Yeah, I think they're more receptive, too. Nonetheless, that's beside the point. I just want to comment on a few more things...
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You do not know me at all. So please do not comment on things that you know nothing about.
Snap!

Sorry, I thought the advice coleb was giving was quite reasonable, but at the same time I'm glad you came to ask this forum about it. Some psychiatrists don't take these stories seriously and you would be ridiculed, which is not good for either of us really, because it doesn't help anybody if the experience is real! I think what your son is seeing is real. I believe they are perceived as shadows, because the form is not fully carved out, if that makes sense. I'm just thinking of Freddie Kreuger at this point, because the man in the hat idea - well, I'm assuming the shadow person is a male - I just think of Freddie Kreuger. Especially since he has a hat and all.
Is is hat yellow though? It's just something that popped into my head and I can't stop picturing this smokey ovular shape with a yellow hat on!

Please don't think I'm taking your situation seriously. In fact, I want to ask something else.
Does your son have communications with this "shadow person"? I don't like calling it a shadow person but to perception this is how they can appear so I suppose it makes perfect sense to call it that. If he does communicate with it, I'm curious with what it has to say because it might give you some clue to how to "get rid" of it. In reality, I don't think you would be getting rid of it. If it's simply energy trapped to the house, then it could easily be removed. Is this a new house? Do you know who owned it before?
I don't think this being will in no way hurt you. It doesn't seem malicious, from what I've heard.
But if there are more than one, maybe ... hmm! Well, here's an idea for you. Imagine white light surrounding your house and affirm to yourself that it is safe, and imagine your house how you would like it to be and -feel- it. I hope this makes sense. Keep doing this. If that doesn't work for you, you could try creating a pendant or something and give it properties which could keep such shadow people away. Keep your living area yours, and filled only with the energies you want there. You can get an object and imagine it being this sort of repeller or bringer of light, if you prefer.
Anyway, that's just a few ideas. Let me know what you think!

EDIT: Oh, whoops! It seems I've gone completely against what the other users have said. Almost. Your home is a good place.

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I would follow what Brightside and I have suggested; stay in the positive and do not pay it any mind. This energy is not a threat but looking for attention. Being that your son can not cope with it considering his conditions he should try his best to rationalize it and put it past him. He must work to create a barrier and essentially work to close himself of to things of that plane. I do not know what your religious beliefs are but I personally remind myself whenever I feel fearful that God is Here and he is within me. And as God cannot be sick, hurt, nor afraid I will not be sick hurt nor afraid. (from Lessons In Truth). If you don't believe the negative, it becomes nothing. It is up to you to find a way teach your son to bypass his fears.
This is true!