The health care benefits and services specified in sections 68-1401 to 68-1406, to the extent that such benefits and services are neither provided under any other federal or state law nor provided or available under other contractual or legal entitlements including insurance of the person, shall be provided to any patient who is a resident of this state and is made eligible by the provisions of sections 68-1401 to 68-1406. After such patient has utilized such contractual or legal entitlements, the payment liability under section 68-1405 shall then be applied to the remaining cost of the genetically handicapped person's services.