Is it legal for your boss to try to force you to sign a different
offer letter with a pay cut and after working almost three months.
It's legal for your employer to ask you to sign the new letter. But you cannot be forced to sign an offer letter.
Of course, there may be repercussions if you don't, including being fired.
I walked into a meeting where I was told that I was being moved to
another department and that I have to sign the new offer letter with a
pay cut.
Unfortunately, reorgs happen (been there, done that). And it's possible that after seeing you in action for three months, they no longer think you are a good fit for your current role. Perhaps this is a way to try and keep you around in a lesser role.
Moving you to a new department isn't against the law. And asking you to take a pay cut isn't against the law.
Again, you don't have to accept either, but there will likely be repercussions if you do that.
He is trying to make me come in on my day off to have another meeting
to try to force me to sign the new offer, is this legal? What should I
do I next?
You don't need to come in on your day off if you don't want to. And you don't have to sign the new offer.
You need to decide if this is the hill you want to die on, or not. If you want, you can contact your lawyer first.
If you haven't already done so, you could agree to change departments, but indicate that you don't think it's fair to have your pay cut. It likely won't work, but thre's only one way to find out.