You can use both sit on a chair or sit in a chair, both are correct. The difference is the type of chair.
If the chair closes around someone then we are are more likely to use IN
If the chair is more open then we use ON
It is impossible to say exactly which types of chairs might use on or in. You can decide to use either On or In.
Here are more examples that can help you to understand the difference but don’t worry if you make a mistake with this. Everybody will understand what you mean!
What is the difference between On and In(prepositions of place)?
In general, we use on for surfaces and in for enclosed areas(Inside and outside!.
Let’s look at more examples:
I am sitting on the floor.
I am lying down on the bed.
Put the picture on the wall.
I watch Game of Thrones on T.V
I will send you a message on Whatsapp.
For everything online, we use on because the screen of your computer or cellphone is a surface.
I work in a big building.
I went for a walk in the park.
I put the tea in the cup.
The ball was in the net.
She put the ring in the cake.
Remember that we use in for volumes/areas. That is why we use in for parks because we think of the area of the park on a map. The same logic applies to a neighbourhood.