"This my chair is new" is:
هَذا كُرْسِيَّ جَديدٌ.
"hadhaa 2al-kursiyya jadiid(un)" - if we follow Standard. But, would the "This my chair is new" sentence be a proper English sentence?
I suppose you mean the sentence is "This is my new chair", right? It will be:
هذا هو كرسيَّ الجديدُ.
"hadhaa huwa kursiyya 2al-jadiid(u)".
(I accept any feedback)