Read your non-compete carefully. Some states have a history of outcomes favorable to the employee in matters of non-compete agreements. So it depends on where you reside and the jurisdiction of the court as defined in the agreement.
But small vendor consultancies, especially desi ones based in NJ have been pitched by the guy, below. So they have now started sending the "Cease and Desist" notice and then the court filing after 30 days (i.e. only if or once your desi consultancy finds out you have taken job with their vendor partner). The template that Patrick sends is pretty standard but it has a tendency of scaring the hell out of whoever receives it. And then once the case is filled in NJ court, you have no other option but either to settle or to pursue, both of which are expensive. Most of NJ small desi consultancies are his clients so sending those standard cease and desist letters are just a matter of changing names in his template (probably only costs him $5 postage). And thereafter, the court filing only costs him $150. The NJ consultancies that have those "Non Compete" clauses installed in your Employment Agreements are pretty much standard, as well. They, I am assuming, are paying Archer, a monthly retaining fee (but not huge sum) and will pay only if the case goes to litigation. In the meantime, if you settle he gets 30%. Win-Win for both Archer and his desi consultancy clients (i.e. your employer).

This guy >>http://www.archerlaw.com/attorneys/patrick-papalia/

(below is just an Internet article on the enforceability of non-compete agreements)
http://corporate.findlaw.com/business-operations/will-your-non-compete-agreement-withstand-a-court-challenge.html

http://www.myemploymentlawyer.com/cgi-bin/mel/app.cgi?action=browse&cat=Non-Compete%20Agreements&type=questions&state=NY

Thank you for your input kalidasbhaisaab

Yup, it is legal. Any client they introduce you to , are considered their business partner and you working for them directly can be considered damage to their business. So they can claim the amount that is considered damage. The second link share by kalidas is what you should definitely look at.

Can they charge anything if I got completely different job nothing to do with their client?

@birey

They(consultancy) cannot do anything in your case. You are safe.

Back to the topic of this thread, here is the catch. If the job deskription was contract to hire then the consultancy cannot stop you from taking the full time regardless of any paper work you have signed with them. You will have upper hand in this case. The consultancy does not have any case against you.