Resignation from first job - after 2 weeks of joining company A, company B has asked for some joining paperwork

Hi, I recently joined an MNC (Company A) after graduating from a prestigious engineering college in India. Actually, I got another offer from company B through off-campus means at a higher package in which I wanted to work, but they delayed the joining too much without even giving a formal document for the updated joining. Considering my family's weak financial situation, I joined company A, due to the fear that if company B revokes the job offer, even the College Placement Cell won't help and I'll be left unemployed.

Now, after 2 weeks of joining company A, company B has asked for some joining paperwork including Relieving Letter etc. How should I tell company A about my resignation, given that they had a probation clause of 6 months during which resignation can be taken without any notice period? Will Company B understand my reason for joining company A? I am utterly confused, because company B has it's joining in Late September or Early October, but is demanding the Relief Letter now. Should I resign immediately or wait?

If you can resign from Company A, without any notice period, as you are in probation period, then what is theproblem?

Hello friend,
First of all you have to check your Terms & conditions for 'resignation' with Co.A when PP is still on. Mostly it will be notice of 'one month on either side', if yes, discuss with Co.B, tell them the circumstances as the catch here is, as you told us, Co B is already insisting for a Relieving letter from Co.A. Where is other option? If there is a enabling clause saying 'notice or cash down in lieu of notice' then go for it. Before taking any decision you should be clear about the stand of Co.B and act upon.

@Rkn61 sir, the problem is I am not very sure how the company B would react. I am afraid they would consider my act as unethical and may even dump me!