who has power to summon the session of state legislature
Governors of states of India The governor summons the sessions of both houses of the state legislature and prorogues them. The governor can even dissolve the Vidhan Sabha. These powers are formal and the governor while using these powers must act according to the advice of the Council of Ministers headed by the Chief Minister.
Special session In a legislature, a special session (also extraordinary session) is a period when the body convenes outside of the normal legislative session. This most frequently occurs in order to complete unfinished tasks for the year (often delayed by conflict between political parties), such as outlining the government's budget for the next fiscal year, biennium, or other period. Special sessions may also be called during an economic downturn in order to cut the budget. In other cases, a special session may be convened to address special topics, or emergencies such as war or natural disaster.