On Tuesday I was told to come to work earlier for my boss because she needed me, I worked 2 hours then she told me she didn't want me to come today early but the next day. But I already clocked in and worked those hours , she said she will not pay me for my misunderstanding her. Is that legal in new jersey/

Its not legal anywhere in the US. Your employer is required to pay for time worked.

" clocked in " so this means you are an hourly employee not salaried, right?

I work in New Jersey at preschool. My time to clock in is 9:00am. But I was asked to work on Thursday earlier at 6:30am to open. On Wednesday my boss was going back and forth between myself and another girl who should come in early and what day. When I left Wednesday I was under the impression I was still working on Thursday at 6:30am. I arrived and 15 minutes later the other girl came in. I asked her why she was there and she said they text her on Wednesday night to come in early Thursday. But they did not tell me not to come. When the owner came in she told me she will not pay me for working early those 2 1/2 hours. I told her I was told but she said the schedule didn't say my name, but they didn't tell me they changed I said. Back and forth we went and she said I will not pay you for these hours worked, I am not paying two people. If it was a misunderstanding or miss communication does the boss still have to pay me? Is it legal to not pay me if I punched in?

Punching in is no guarantee of getting paid. Sadly, this is a he said/she said and you can either fight it with copies of phone tapes or emails in small claims (but you don't have any), or try to use reason with the employer - or quit. It does sound like she might have said something along the lines of she'd let one of you know that night, and you missed it. I'd be inclined to let it go and just never get into any off schedule hours again.

I've merged your threads, please don't start a new thread for the same issue.

This is a different story than originally told. If they can prove that you were not on the schedule, then they may have grounds for not paying you.