Wherever I apply, I get a response that they are moving ahead with some other candidate, I don't even get a call for an interview, even though the job description matches my profile. How are you getting the calls?

I used to apply through the openings posted on LinkedIn, naukri and similar job portals. I tried sending an email to HRs finding it on career pages but unfortunately negligible response. I have tried multiple times to upgrade my resume in hope that it will work better but the result is the same for every time.

Applying directly on job openings may not fetch you interviews unless you are extremely lucky. Instead, try sending connection requests to recruiters/hiring managers/directors of a company. If they accept your connection, try pinging them with your cover letter and asking them if there is any opportunity in their company.
If it's a hiring manager or director, they can give a referral. The referral would probably be much more valuable than the referral of any junior employee in the company. If it's a recruiter, then direct interview process.

But do keep your expectations low. Expect only 1% of the people will reply back. Keeping sending connection requests daily.

It's a tiring process, so don't give up easily. No need to send in-mails. I don't think you also need linkedin premium for this approach.

Thank you for taking out the time to write here. This really helps me a lot! I will review my resume and profile on the job portal and make some changes for sure.