I have already joined the new company and have been working for the past 10 days but I haven't received any offer letter or salary breakage slip yet. Is it better to quit the job or continue. I don't know what to do. What will be the problems that occur when I leave the job.?
Never quit a job unless you have a new one or you know you're not going to get paid.
Check with your manager or human resources, when will you be getting paid. If it's not too far in the future then just wait. If it's too far then find out how much.
Chalk it up as a good lesson for future jobs to make sure you have some sort of agreement before taking a new job.
Always be looking as an employer can drop you like a hat for any reason. Always look out for your own interests.
First of all: You do have a contract, so don´t just stop showing up anymore. Unfortunately you did not provide your country, but the base concept is the same in most developed places: You showed up and delivered your work, and they happily accepted your contributions. So you now have kind of a silent agreement that you basically work there.
The problem is, non of the parameters of this contract are defined right now.
If you decide to stay, see that you get those parameters defined, in writing, as soon as possible. You are in a good negotiation position since they already took you on board. State your terms and only sign once the offer is acceptable. Most importantly: Salary, work-times, vacation, and notice periods.
If you want to leave, write a formal letter of resignation and inform yourself if there are any required minimum notice periods in your local law which you ma have to keep.
If you are in doubt weather they treat you fairly or they wont pay you or anything seek legal support. Chances are they ow you some money!