What was the gotra of gadAdhara/ rAmakRShNa-paramahaMsa? I tried searching on the internet, but did not find a clear answer.
Sri Ramakrishna Paramhansa before taking sanyas was known as Gadadhar Chattopadhyay. The Chattos(Chatterjee/Chattopadhay) are Kulin brahmins who were called from Kanyakubja by Adisura , a King of Bengal. Total of five brahmin families came from Kanyakubja, Chattos is one of them. The Chattos have gotra Kashyap, They belong to the Rarhi clan of brahmins.
Another thing, Sri Ramakrishna Dev also had tantrika initiation. It is said after tantrika initiation a person is given a new gotra. I have heard that then he was given Parambrahma gotra one of the trantrika gotras. However not sure of this tantrika gotra system.