I just started a job with a hospital in Brooklyn. I am under doctors care as of two weeks into my job. I've been terminated as a Probationary Release. What does that mean?? The letter stated being that I was unable to complete my probation, my position was terminated...

I didn't know this was legal.

There's a widely held misconception that you can't be terminated with a doctor's note. Unless both you and your employer are coverd by the Family and Medical Leave Act, which provides 12 weeks unpaid leave with job protection, then the employer has no legal obligation to hold your job. You mentioned that you were on probation and only recently started; one criteria for FMLA is that you have to have been employed one year.

It just means you were terminated during your probationary period - very legal under doctor's care or not.