The details of Ownership structure on the website of Media Ownership Monitor India refutes the claim.
The webpage mentions that Arnab Goswami is one of the co-founders of Republic TV and is an outlet of Arnab Ranjan Goswami (ARG) Outlier Media Asianet News Private Limited. Mr Goswami is also the Director of ARG. The company is a subsidiary company of Samyabrata Arnab Ranjan Goswami (SARG) Media Holding Private Limited which is again founded and owned by Mr Arnab Goswami along with his wife Samyabrata Goswami.
Thus, it is clear that the channel has no link to any BJP leader.