It’s not unusual for individuals with schizophrenia to be paranoid even when they are taking medication. Medication works to prevent most of the symptoms of the disorder but it is not uncommon for there to be residual symptoms.
If I had a chance to ask you follow-up questions about your letter I would want to know if your mother’s paranoia is a new symptom, something that has recently intensified, or a condition she’s always experienced. If it were a new symptom or a condition that has recently increased in frequency or intensity, then it may mean she has stopped the medication. It might also be a sign she needs her medication adjusted. If she stopped the medicine, then it’s imperative to try to get her back on it immediately. If her medicine needs to be adjusted then this information needs to be conveyed to her doctor.
If you’re simply asking about how to deal with paranoia then one way is to continually reassure her that nothing has gone missing. You can try to prove this to her by showing her that in fact the items she is concerned about remain in her possession. You may have to do this repeatedly and it might challenge your patience but it may be the only way to reassure her that her things have not been stolen.
You mentioned that you put an alarm system in the house and changed the locks. Those were very smart ideas. They also show your care and concern. You should continue to remind her that you have done these things.
As I mentioned before you may want to explore whether she has stopped taking her medication or if it needs adjusting. You should also alert her doctor about the paranoia. Her doctor may be able to give you additional advice about how to deal with this situation.
I’m not sure if my advice will be helpful because you did not include much detail in your letter. If you would like to write back and add more information I would be glad to try and answer your question with more specific suggestions.