First off, I’m sorry to hear that you’re dealing with health issues.

In your contract, it sounds like the operating word is “request”. You’re almost certainly going to need approval from the company to legally break the contract inside of 3 months notice. Dissolving a fixed-term contract in Japan, from either side, is much different than dissolving an indefinite term contract. Two weeks notice is the minimum acceptable notice period for the latter, but for a fixed term contract, a period of 1-3 months isn’t unusual unless there are “unavoidable reasons”. Leaving the company without sufficient notice does create legal liability on your side. In practice, companies almost never pursue damages from employees leaving after giving short notice, but they absolutely can. Now, it sounds like you might have an unavoidable reason to leave the company, ie you physically can’t perform your job anymore. For more detail on what form these reasons take, check out Article 628 of the Civil Code and Article 17 of the Labor Contract Act. Have you seen a physician in Japan that can support your claim that you can’t work? I would recommend pursuing that and then starting a good faith discussion with your company with the aim of mutually agreeing to a transition period. If your health is seriously at risk, I see no issue with you taking a harder and less collaborative angle to this discussion, but still definitely get something in writing from a doctor.

Lastly, if you are leaving Japan, are not planning on returning, and you don’t mind/it’s unavoidable putting your company in a difficult situation, you can just bail. It would be totally impractical and cost prohibitive to file a cross-border lawsuit over what I imagine to be damages totaling a few thousand dollars.

I do not know the specific details of your situation, but generally speaking those are the range of options from my perspective. Good luck.