NY has fire at will here is how it works... it goes hand in hand with whats called employed at will....

employed at will means a person has been hired for a certain job or time frame . when the job is complete or the jobs time frame has expired a person is laid off/ let go or re employed for a longer time frame or another job with the same company.

example christmas season many stores employ extra employees to meet the demand of the public. when christmas season is over those employees are let go/laid off due to the job is no longer available or has expired.

but with this also comes a situation where an employer can make a temporary employee permanent if they choose to by signing a new contract...

example a store employer notices how well an employee works with the public, comes to work on time basically is an asset to the company and the employee knows that in the future there will be people retiring or leaving due to what ever reasons. they offer the temp employee a permanent position complete with a full time paycheck and benefits if the job comes with that.

that is what "hiring and firing at will" means here in the USA. employers cant just fire someone for no reason but there are special terms of contracts and such that comes with being hired as a temp (temporary employee)

if you feel your position was not a temp position and were fired unjustly or at will you can contact your labor union/ labor commission / temp agency that sent you to the job placement/ local unemployment office/ or the civil rights department. any of those can help you to investigate the terms of your employment and whether the company has fired you illegally. they can also help to prosecute employees that have illegally fired you.