What do I do when my significant other basically always thinks I’m lying about anything having to do with cheating or wanting to cheat when I’m not, even things that happened literally years ago?

Show your love by arranging a gift and spending more time with him/her. Give him/her the password to your phone so they know they can trust you. Spending time with your significant other is always a great way to show you care. Anytime he/she is facing problems, be there for her/him so they know you are there. If none of these work, talk to your significant other privately and calmly address the situation. Tell your significant other that you really are not cheating on him/her. Apologize for anything you may have done in the past. If all else fails, ask what you can do to make him/her trust you completely.