@Arun Azure SQL MI can be configured as a publisher with your on-premises database as a subscriber.
Please check this tutorial for more details.
You will have all the benefits of a managed database on Azure while still being able to replicate to your on-premises database.
If you need transactional replication, please ensure that you have a low latency connection over express route between your on-premises network and Azure so that you don't face any issues.
If you want to use SQL Server on Azure VM's, configuring log shipping is no different from doing it between 2 VM's on premises.
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