Now I am planning to quit the job in this company.
Good better late than never.
If I get the job in the other company what should I answer if they ask Why are you quitting the previous company and they asked for the documents like offer letter and relieving letter and pay slips.
You can tell them the truth. Most probably what they will be more concerned is about the work that you did there. So that they can see how you can be a suitable candidate for the role applied.
Other than that they can ask question like why did you work for free, how did you support yourselves for that period etc.
Most likely they will have their own systems in place to check whether the candidate is qualified to do something other than just believing past employment proofs like offer letter, pay slips, relieving letter, etc.
What if I continue for one year in the existing company without salary and quit the job?
If I was in your place I would quit. I am not sure if you brought this topic to their attention or not but it's their business to see if employees are compensated or not. If they haven't discussed it yet there is a high chance they won't discuss this with you in future.
What are the consequences I will face in the future?
Not much other than lost compensation for the period you worked.
Since I started my job career recently so I am confused for the next step
Next step is to get things in place and get a job that pays unless you want to work for free.