I came to US and worked at a University, holding H-1b visa. For the past three years I paid taxes (federal, state, city) very year and recently I heard that H-1b holder could have taxes exemption for three the first three years. Is that true? If that is true, can I get the money back?
Thank you

As a general rule, no. However, depending on which country you are from, the treaty sometimes permits the income to be excluded from tax. Also, it usually applies only for a limited time and is sometimes not available if you stay too long. I'd need to know the country and what you are doing.

H1-B is work visa. There is no treaty benefit on this income.

H1-B is work visa. There is no treaty benefit on this income.

This is not quite accurate. This is true generally of the treaties but is typically not the case with respect to certain articles (for example income as a visiting professor).

This is not quite accurate. This is true generally of the treaties but is typically not the case with respect to certain articles (for example income as a visiting professor).

Visiting professor won't get H1-B. They will get J1 visa for professors and researchers.
H1-B is work visa, and there is no treaty benefit on this visa.

Visiting professor won't get H1-B. They will get J1 visa for professors and researchers.
H1-B is work visa, and there is no treaty benefit on this visa.

Usually the case, but not necessarily so.