What you are dealing with is one of the most common and most painful dynamics in prison relationships, and it has almost nothing to do with you.
When someone is incarcerated, they lose control over virtually every aspect of their life. What they eat, when they sleep, where they go, who they interact with. The one thing they feel they should still have some connection to is the person they love on the outside, and they cannot control that either. So the mind fills the vacuum. An inmate sitting in a cell with nothing but time can construct elaborate and completely fictional versions of what their partner is doing, and the more they love you, the more those thoughts can spiral.
I lived this from the inside. I was convinced my wife was running around on me. In reality she was working herself to exhaustion keeping the household together and our kids fed. Every accusation I threw at her, every argument I started, every jealous spiral I put her through, I created all of it in my own head. It took me a long time to see that she was not living her best life without me. She was grinding through it, waiting, holding things together alone. When I finally understood that, the accusations stopped. Not because anything changed on the outside, but because I stopped letting my imagination run the relationship.
What helped from her end was consistency. She kept showing up, kept writing, kept answering the phone. She did not match my energy when I was irrational. That steadiness over time is what eventually got through.
You cannot logic someone out of prison-brain insecurity. What you can do is stay consistent, keep the communication warm and honest, and remind him through your actions over time that you are riding this out with him. There is real hope here. Some of the strongest relationships that exist today were forged exactly in this kind of fire.