Can landlords make me sign paperwork and tell me to date it 14 months ago?

I live in a govt. subsidized apartment. My landlord screwed up on the paperwork from the last lease. They want me to now sign paperwork that they should have had me sign on the last lease, and date it as if I signed them in August of 2008. i think this is called solicitation. trying to get me to do something that is illegal. Am I right? I know this is illegal, D.A. said it can be considered extortion. Is there merit for me to take them to court and sue their bigtime corporate s? They said I could not sign the new lease unless I did this. The used inuendo to try to tell me they may serve me papers to leave if i don't do it. Does it matter if it is govt. subsidized? They could lose their ability to be involved with govt subsidized housing/ I am a poor teacher, have any advice. I know I should get a lawyer and ask him/her. I will I think, just wanted your advice...any attorneys' out there that can give me their opinion? Thanks much! Had a dream I won a million from these b*stards!