As to your question "how to report this (federal, state taxes) in TurboTax?" the answer is "you don't because it's already been reported on your W-2." You had a "same day" sale of stock (vesting/sale on same day) "for taxes" and that cash was passed back the the employer, who paid the government(s) and included those amount in the various "taxes" boxes on your W-2. You can check with your payroll department.
If the broker had withheld and paid the taxes - called backup withholding either because you didn't submit a W-9 or did submit a W-9 and said you were subject to backup withholding - it would be on your 1099-B.
"Also, on my W2, a slightly lesser amount is given with code V in box 12B, than what is reported on 1099B."
I assume what you are saying here is that the proceeds on the 1099-B is greater than the dollar amount of the W-2. All that means is your employer used a slightly smaller per share "fair market value" (and reported slightly less compensation income) than you actually realized when you sold and it's no big deal. Forget about it. You'll use the Box 12 amount to determine the basis for the sale and realize a slightly higher short term capital gain. Trying to get it "corrected" amounts to pushing small numbers between "compensation" and "short term capital gain" both of which get taxed at the same tax rate.
Tom Young
