Welcome to LQ. I understand your query being the same countryman.
I am working with linux from 1 year.
I'll safely assume you have been working on RedHat Enterprise Linux or Ubuntu as in India a general mass consider Linux as simply RedHat Linux or these days Ubuntu too.
If you want to get certified with employment specific reasons, would suggest you to go for RHCE certification. There are other vendor specific certifications for Unix-based products like HP-Unix, IBM-AIX, Oracle-Solaris etc, however my suggestion would be RHCE first.
Vendor free in laymen terms means the product is not locked to/property of any specific vendor, generally educational organizations conduct these ones, I'm not aware of anything except LPIC (which holds no particular recognition in India as far I saw).