The bosses of some of the start ups, in general, try to live up to the meme " Rule 1: The boss is always right Rule 2: If the boss is wrong, see Rule 1 ". They are their own Prime Ministers and as such they have scanty regard for good professional standards or legality of their actions. Therefore, in the current scenario you described, it is for you to decide whether you want a smooth exit in view of a peaceful future employment or prepared for a show down.
Even according to the so-called "letter of intent" issued at the time of joining the start up, the probation is for a period of six months comprising of a notice period of one month only and you would be issued a formal appointment orders after the said six months. However, as per your statement, even after completion of more than one year service in the same organization, no appointment orders was issued. It implies that still you are a probationer in the absence of a formal declaration of your probation and as such it is suffice to give one month's notice on your resignation.
So, write this back to him politely and request to relieve you on the expiry of the notice period of one month failing which you would be simply walking away.
11th December 2018 From India, Salem