H1B employer (consultant) says they will sue me if I do not pay the H1B filing fees.
I have already left that company.

It is illegal to make employee pay for h1 filing fees. You can contact department of labour for further details. So you don;t have to worry

What i mean by filing fees is the applicatoin fee and the lawyer fee.

So is it illegal for both cases or just applicaton fee case.

No one can sue you dude..
#1 they are not allow you to put in contract.
#2 its their job to get to H1. so you don't have to pay for it.
If they ask for money it is illegal. (they are just simply providing H1 to anyone for money.)

instead u can sue them saying they are asking u for money.

The Department of Labor (DOL) requires the employer to pay the legal fees associated with the preparation of the H-1B visa petition and, if the employee pays these legal fees, the DOL considers such a payment to be an unauthorized deduction from the employee's wages. The H-1B filing fee is comprised of three distinct components: (1) a $190 filing fee; (2) a $750/$1,500 H-1B training fee (with the amount determined by the number of employees employed by the Petitioner); and (3) a $500 anti-fraud fee (which only applies to first-time H-1B petitions and change of employer petitions). It is the employer's responsibility to pay the H-1B filing fees. Should "premium processing" be requested, the additional $1,000 premium processing fee could be paid by the employee or by a third-party.

Source: http://bostonworks.boston.com/hr/hrexpert/articles/111405.shtml

Similar sitation here too...

What if one never joined the company.
Working for company A and during that time filed H1B with another company B. Project got extended with company A and never joined company B. But continued to look for projects through company B for six months but never landed in a project.

Now is it the same thing, or different since I did not join company B.

Thanks to NiloAkash for posting the website.