Clan : Chandravansh
Gotra : Kaushik
Kuldevta : Bhagwan Shiv
Kuldevi : yogeshwari Mata
ved : yajurved
Thi is for Kaushik gotra
Similarly every Gotra has its own Kuldevi, which is basically Bhagvati, Bhavani. Maratha king Shiva ji is from Kaushik Gotra. Kaushik Gotra is basically from Viswamitra Rishi descendants.
Brahmarishi Vishwamitra’s was a king known as King Kaushika, he was a Kshatriya who was attracted by Kamadhenu in Brahmarishi Vasishta’s ashrama.
Vishwamitra became a Rajarishi first and later became a Brahmarishi. When he became a Rajarishi, his name remained Kaushika and hence the people who refer to Kaushika as their gotra are the descendants of the Rajarishi Kaushika. The people who have Kaushika gotra can belong to either Brahmin or Kshatriya communities. And when he became a Rajarishi, he was in Mithila, a place in Nepal. Hence, people in the South and the North have Kaushika gotra. Maithili Brahmins, Kanyakubja Brahmins, Kashmiri Pandits, Deshastha/Madhwa Brahmins, Koknastha Brahmins, Vaidik Brahmins, and Niyogi Brahmins have this gotra. Not only this, 11 Royal clans of 96 clan of Marathas belong to Kaushika gotra including the illustrious house of Shivaji and the Rashtrakutas.
Vishwamitra gotra used by the descendants of Brahmarishi Vishwamitra, that is after he was blessed by Vasishta to become a Brahmarishi. Unlike Kaushika gotra, this is used by only Brahmins. It is one of the most important gotras for Brahmins and Madhwas and Deshastha Brahmin from Karnataka, Maharastra and Tanjavur have this gotra.
Both refer to the same person, the great Vishwamitra who is the only Brahmarishi to have earned the title through penance. The rest of the Brahmarishis are direct sons or manasaputras of Lord Brahma. Vishwamitra was the one who composed the great Gayatri mantra. The starting two lines in Venkatesha Suprabhata are said by him and look how beautifully he wakes up Lord Rama.
कौसल्यासुप्रजा राम पूर्वा संध्या प्रवर्तते ।
उत्तिष्ठ नरशार्दूल कर्त्तव्यं दैवमाह्निकम् ॥
kausalyāsuprajā rāma pūrvā sandhyā pravartate ।
uttiṣṭha naraśārdūla karttavyaṃ daivamāhnikam ॥
O Rāma, the noble son of Kausalyā! The Sandhyā of the East commences. O! best of men (Purushottama)! Wake up, the divine daily rituals have to be performed
Only way to find out is from ancestors and Purohit of your villege otherwise it is impossible to find out.