Can't use mTLS with API endpoints

Recently I set up mTLS on my admin endpoint. I tried entering it as an API on the other website, and in Firefox it wouldn't work. But if I'd try to access endpoint directly it would work, and even save my certificate choice. In Chrome, everything works just fine with both direct and API access. It is not a problem of a website, nor the problem of the OPTIONS preflight, since both of those are configured correctly on my nginx.