I sign my lease and now my landlord wants me to sign a addedium

I think you're referring to an addendum, which is an addition to an agreement. If you already have a fully signed lease then you don't have to sign the addendum because the landlord can't change a fully-signed lease without your consent.

If you've signed but the landlord hasn't signed yet then the landlord can require that you sign the addendum. If you don't sign it then the landlord can refuse to sign and doesn't have to lease to you.

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If you've signed but the landlord hasn't signed yet then the landlord can require that you sign the addendum. If you don't sign it then the landlord can refuse to sign and doesn't have to lease to you.

That would be a different question, and the answer to that question would depend.