When a down and out loser discovers a time portal where he communicates with his arrogant younger self, they attempt to create a lucrative future together, but become mortal enemies and a battle for control in this alternate reality drives him to the brink of psychosis. Refraction is a 98 page feature, psychological thriller in the vein of The Butterfly Effect or Twilight Zone.

Interesting concept . This could be tricky and could take the "loser" into many directions. The "loser" should be likable as to make the audience want to "pull" for him. Or they may lose interest if it gets confusing .

Defiantly remove the note at the end these types of comments are best reserved for a pitch not a logline.

The remaining logline describes a situation and a vague plot. What is the main character trying to achieve? Better yet what is he fighting for? Control in an alternate reality is not a clear enough goal for the MC to pursue.

The inciting incident described is the discovery of the portal, following this as the starting point for the story, I find it hard to imagine what the end of the story is. Battling for control in an alternate reality is too vague an action for a logline.
How does he battle? This will constitute most of your act 2 and therefore most of the film you really need to be clear on what this action will be.

It is also difficult to identify the genre it sounds like a comedy from the first half of the logline but then with the introduction of the psychosis it tends dramatic in feel. If this is a comedy better to drop the psychosis but if a drama then best to establish it earlier on as an obstacle perhaps as part of the MC description.

Hope this helps.

I am guessing the note at the end isn't part of the logline, if it is drop it off. Great concept, but the wording is clumsy.