Unfortunately you haven't provided enough details for anyone to give you a meaningful answer to your question; furthermore, any competent answer will depend on a lot of different facts, including personal information that you probably don't want to post in public, so if you want an accurate answer I'd strongly suggest that you speak with competent local tax counsel, such as an accountant or a return preparer (no need to go to the expense of a tax attorney based on the circumstances you've discussed).
That being said, assuming the entire settlement is subject to tax as wages (generally where the highest tax burden exists), and given that you apparently live in New York City, the total tax withholding, including income and payroll taxes, would most likely be no more than about 46% (assuming you had so much other income you were in the top income tax bracket). As such, under those conditions, if the gross amount of the settlement is $6,800, then the amount of tax withheld would be approximately $3,128, leaving you with a net amount of approximately $3,672.
A bigger question in my mind is how much of that is going to go to the attorney(s) who negotiated the settlement. If the settlement was from a contingency case, then it's quite possible the attorney(s) would keep 30% of the gross settlement - that is, before taxes are withheld - or about $2,040. Furthermore, the person paying the settlement will most likely compute the tax withholding without subtracting out the attorneys' fees, which would mean that they would still withhold about $3,128 in taxes. Taking all of that into account, under a very conservative, adverse estimate, the net amount of cash you would probably get would be about $1,632 ($6,800, minus $3,128 = $3,672, minus $2,040 = $1,632).
Hope that helps.
My answer does not constitute legal advice and may not be relied upon by anyone for any purpose and does not constitute an attorney/client relationship or an offer to form such a relationship. This disclaimer is intended to be fully compliant with the requirements of Treasury Department Circular 230 and the terms thereof are fully incorporated by reference. If you wish to consult with me please contact me at dwatchley@newyorktaxcounsel or visit my website at www.newyorktaxcounsel.com
I think Dana's answer is on point and fully covers what you need to know. May I suggest as a practical matter that you contact either the attorney who helped you secure this settlement and/or the party sending you a letter stating your share and pose the question to them. It sounds to me like you may have been part of a class action, in which case, there may be a class action counsel to contact.