Hi
I am on a H1 Visa and I am just arrived in the US.
My employee takes off from my paycheck the money
For the Medicare and for the OASDI tax.
I was aware that for the first two years in the US
I don't have to pay the above taxes. Is it true?
Is there some restriction for the H1 visa?

Thanks

No, it is not true.
On H1-B you must pay SS tax and Medicare tax right from your first pay check.

Agreed; the two-year exemption of which you speak apply to those who are under a J-1 visa.

For F-1 visa holders, the exemption time frame is five years.