It is not clear if the good job you refer to is the one involving the contract you signed or not. I recommend that you contact an attorney to discuss your situation in more detail.
I am sorry, I am not entirely clear from the text what actually happened. I suggest you give an employment attorney near you a call and discuss this in a little more detail.
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As the others have pointed out, your question is not entirely clear. However, is your main concern that the "contract," if enforced, will cost you money each month (for a year) in the form of a payment to the company for finding you the job? If that's the concern, you will have to make a business decision as to whether the cost over time is greater than the imminent loss of your job, which you admit you like.
(1) I may be guessing. Do not act or rely upon this info; (2) We have not established an attorney-client relationship; and (3) If you insist I tell you something upon which you can actually rely: don't eat yellow snow.