If u live with someone in an apartment with an exspired lese and a month 2 month rent is now being paid and an eviction notice was served to the prior leser what kind of "squaters rights" does this someone have.

There is no such thing as squatter's rights.

If you are living in an apartment where the lease has expired then you are a month-to-month tenant. The only rights you have are the rights of a month-to-month tenant as per the laws of the state where the apartment is located.

If the landlord has issued an eviction notice to the prior tenant of the apartment then that eviction notice would also apply to you, as long as you were made aware of the notice. If the landlord provided the amount of time required by law for you to move out, and you fail to move out, the landlord can file a lawsuit for eviction. If you do not have a defense to the lawsuit then the landlord will win a judgment and can have you evicted by the sheriff or constable.

There are no squatter's rights, if the prior tenant left and you stayed in the apartment the only right you might have is for legal notice to vacate. If the landlord is willing you can sign a new lease.

'rent is now being paid' - to whom?
If the landlord, then you are better than a squatter, which as stated doesn't exist. You are now a tenant at will, or month to month. When a landlord accepts a full month's rent, you are automatically a tenant. Law goes by state, but I am not aware of a state where that is not true.
Make sure you have proof of payment. If cash, get a receipt!

No rights, you can go talk to the landlord, when the rent is paid, and ask them if they still plan on eviction or not. It is totally up to the landlord

She does have rights. She is not on the eviction notice and it's not clear that the landlord is following through with it anyway, since that person is gone. When he accepted her rent (if he did), then he would have to file a new eviction on her. Which he can do, even if he accepts rent...