Is it permissible to forge a residency certificate for the purpose of transferring one's son to a better university?

If the system prevents students from outside the region from entering universities for a public interest, then it is not permissible to circumvent it by obtaining a forged residency certificate, as this is deception and forgery forbidden by Islamic law. However, if there is no system preventing that, and your son is wronged by being denied study at that university, then there is no harm in circumventing to obtain his right.