How can one be purified from the sin of a doctor taking money from patients in exchange for unnecessary additional examinations?

Your action of taking money from a patient under the pretext of examination without performing it is consuming people's wealth unlawfully. This necessitates repentance by returning the money to its owners, expressing remorse, and resolving not to repeat the act. As for stealing public funds, if the intention is to take something from them without right, it is not permissible. The way to absolve oneself of its liability is to give it as charity to the poor or for the general welfare of Muslims, along with giving out what is most likely to clear one's conscience. Allah says: (So fear Allah as much as you are able).