LinkedIn is a great tool for business in which I've used to get connected to local professionals:
Networking (focusing on professionals & businesses)
Establishing Brand Trust (work in a specific niche market? LinkedIn has the community for you to connect with)
Establishing Authority by Promotion (like all things in life you must give before you can take so joining any groups that are relevant to you is extremely profitable, just think about all the people you could be working with under your niche market if you only joined the same groups as them)
Feedback (whatever product or service you provide is bound to be a success if you ask the right questions & use the answers you receive to provide more value to the marketplace)
LinkedIn has personally connected me with people in the computer science, graphic design, and entrepreneurship industries to name a few.
The best way to become a relevant answer to people's wants and needs on LinkedIn is by becoming someone people look up to & value. Your experience & knowledge are things people want & need to know about so do your best to provide value through your skills and talents while being open to opportunities with new people.
Don't end any contact relations you develop, wait until there is a moment of leverage in which you can provide even more value after you've initially made contact with a lead, customer, and or client; this is when you need to up sell by providing value that they cannot get anywhere else.
LinkedIn is made for professionals and businesses for a reason, don't think just because you've wasted time before with LinkedIn that you can't get the next best opportunity within the platform.
Is there another way to apply for quality jobs?
Employers want to see your skills & talent firsthand. Have a portfolio or resume that's easily accessible online.
A website, video, or even a picture about who you are and what you can do goes a long way to all employers.
That being said, no matter the application process you want to diversify your efforts; don't put all your eggs into one basket meaning if you used LinkedIn again you'd want to try something like https://www.artstation.com in which you can find jobs & the next best opportunity for you & your work to be seen.