Recently my employer payed me a salary adjustment. I though it might be an error so I contacted HR. HR assured me it was my money and I was entitled to it. Now they are telling me it was in fact an error and I have to pay it back. Since I have proof in writing of them telling me it is my money am I required by law to pay it back? Are they allowed to deduct from my paychecks until it’s paid back?
In addition to what D Stanley commented (is it truly a mistake or are you entitled to the money?) also consider how much money, in terms of months of pay? Did you spend it?
If it's a small amount and you did not spend it, then I recommend paying it back and smoothing the relationship with the company. If you spent it, then work with them to ensure a payment plan that allows you to repay as quickly as possible without causing financial hardship.
If it's a large amount, and you're willing to sour your relationship with the company, you can pursue legal action. If it's truly a mistake, then without a written copy of what HR told you, it will be significantly more complicated to win this.
If you are leaning towards taking legal action, ask if it's still worth it giving up 1/3 of the "windfall" (before taxes).
If you still want to pursue legal action, then it's time to visit a lawyer. Though you can probably ask the root question in law.stackexchange.com and get some actual lawyers' viewpoints based on case law.
One is you can ask that they check again - twice they said the money is yours, once they said it isn’t, so you are owed an explanation.
For the repayment, it is important whether you reasonabley relied on the promise and what damage that reliance cost you. Say you moved to a more expensive home because you received a raise, then you would negotiate with the company how much this is their responsibility. Since you even checked that the raise was correct, the company should help you covering any damages.