Is it permissible for a radiologist to agree with other doctors to send patients to her center in exchange for a percentage of the fees, and what is the ruling on the money earned from that?

If an agreement has been made between the center owner and the doctors to refer patients to you, then there is no harm in examining them, and your salary is lawful because it is in exchange for a permissible benefit, and it has no connection to the agreement between the center owner and the doctors.