Everything can be suspicious to the paranoid person. There is one thing you can try and that is to put doubt in his mind about the idea. That is about the best you can do. You can say that you've tried and tried to convince him that you love him and are faithful, yet he still doesn't believe you. Talk to him about where you go and what you do if you wish, to convince him of your innocence, but understand that doubt, not conviction of your innocence is the best you can do at this point.
Medication can help.
It's been recommended he be hospitalized, he won't go. I see my only choices to be - commit him, accept the way he is, or leave him. If so, then you may need to hospitalize him for his own good. Or leave for your own safety. Or threaten to leave if he won't get the help that he needs.