2 Answers
I don’t think it is recommended to backup from AWS to on-premises, this solution will cost you, as you’ll be charged for the data transfer See pricing page https://aws.amazon.com/ec2/pricing/on-demand/.
Can you provide a bit more details as to which resource is in question? What type of storage S3 or block storage? Id look in to volume gateway, where dataset is stored on site and cached on the AWS side.