One characteristic of paranoia is that it is an entirely closed system - new knowledge or information cannot change the beliefs of the person with paranoia. Everything becomes more evidence for their delusion (my ex has these tendencies). So there may be no point in defending yourself or trying to use reason to change these beliefs.
If your ex is paranoid, it won't have any effect on him (it will in fact produce more proof, in his mind, that you really are sneaking into the house), and if your son has to go along with his father's beliefs in order to maintain his relationship with his father, whom he lives with, your son will not be receptive to anything that challenges the delusion either.
In your position, what I've done is just state once that I am not doing what I am accused of doing, and then leave it. You can't reason with someone who lives in a closed system.
Last edited by Sasha1972; 02-13-2019 at 09:02 PM.
Reason: sounded too much like armchair diagnosis