If I want to rank better in local SE (.in/.uk etc) we need backlinks more from local sites. But which is needed Local IP or links from Domain Extension ?
If your server is located in the USA and New York in particular, then you will have an increased chance of obtaining higher rankings for a keyword phrase that is unique to that State. However, the domain does not make a difference here. Whereas, if you were advertising a uk based company website and you wanted to obtain a higher ranking with the uk part included in a keyword, you will have an increased chance of ranking higher than you would do if it was just a standard .com domain.
wow If you are right about servers that is news to me, honestly I cannot imagine with huge companies like godaddy out there hosting millions of sites, IP has ANYTHING at all to do with it. I would spend your time gaining links from local sites
He is asking about the domain extension itself, and yes cc-TLDs do rank better in their respect geographical area.
Links from local site or anywhere else both are important but relevancy should be there and yes local links are help more to get ranking