Does Sugar API v10 support for On-Premises ?

Hello Ajith R, 

Sugar API is available both on Cloud and in OnPremise installations. 

An easy test to check if you are being able to reach the API is to access the URL:

https://<site_url>/rest/v{version}/help.

After that you can start authenticating.

I hope this helps.  

Ajith R,

Make sure you take a look at this (https://support.sugarcrm.com/Documentation/Sugar_Developer/Sugar_Developer_Guide_12.1/Integration/Web_Services/)

v10 is pretty old version and you should be using v11 (and it's variant which increases in every release).

our latest is v11_17 as of now..