Good question. They all work, but it depends on the kind of chair. For stools (and chairs without arms) when there is nothing around you, you can only say that you’re sitting ‘on’ them. For chairs with arms, you can say either that you’re sitting ‘in’ or ‘on’ them.

I am sitting in/on a/the chair - these are all correct. 🙏

'I am sitting on the chair' is correct as you have included 'the'. A general rule (of which there are exceptions!!!) is that you don't use singular countable nouns alone, without an article or other determiner. 'I am sitting in chair' is incorrect, but 'I am sitting in the chair' is correct.