Last year, I made a mistake and mistakenly put my State refund in the line 'taxable interest'. Even though I had my calculations were done without it, NY State sent me a letter with the adjusted figures.

I responded back to the notice but heard nothing back. I lost on some $50 of my refund.

Also last year I filed an IT-203 (Non resident) but this year I am a resident.

This year do I file an amended return? Perhaps Protective Claim etc? I am a little confused here.. Help would be appreciated.

You have to amend the 2013 NY state return to correct the error.

Then would I also have to amend my 2014 federal return as well then? Cause I itemized my federal for 2013 so the state tax refund is taxable.

Yes, unless the IRS catches the error and adds the state refund to your return for you.