I'm sure you know this, but probably your only shot of doing this with such a small time investment is getting out-of-India work.
I personally love contracting, but it's hard to get the work started at first, and it's all about relationships. If you don't have relationships with employers or others who need your skills, your chance of finding online/remote/contract work are very low. Sites like Guru, Fiver, etc. are really all about ultra cheap garbage work, and that's not the market you want to be in.
Long story short, this may take you time, and you need to build your relationships to make this work. Are you only skills web related, or do you have software engineering experience too?
Given your list of skills and experience, perhaps once you have built some relationships with some employers, perhaps you can position yourself as a "off hours support team" for one of them. There are probably a lot of small to medium eCommerce sites that would gladly pay a couple hundred a month to have you on retainer to respond to support emails and troubleshoot site issues. The key here is building the relationships needed to get that kind of work. If this is a niche you are interested in, perhaps you could target a small set of niche sites that are based on CMS' that you know, and contact the owners to try to get an in to perform this kind of support. It will probably take a lot of cold calls (and you should call rather than email, as that would come across as spam) to find a couple customers. Alternately, if you've done any work in the past for sites, you could reach out to those business owners with a compelling reason they should hire you for this kind of work.
Basically, I'm saying find a US or EU employer and use the time difference to your advantage. That's what I'd do, anyway.