I live in FL. I moved in 28 days ago and signed a rental agreement for a year. The landlord presented a supplemential lease with additional terms ( some extreme) for me to sign today, I refused. The landlord said to take these terms and sign or leave. I know this is illegal; but I don't know what it's called or the state statue that prohibit this illegal act. Help.

No, just tell him you are sorry but you have a valid lease, He can not evict you without taking you to housing court, if he tries, just fight it in court, make him prove that you broke any term of the real lease