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.