Azure SQL Database
An Azure relational database service.
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can we sync only last two month data from Azure SQL data sync hub DB to member DB having several years data, i mean conditional sync?
You cannot filter rows or have a conditional sync using Azure SQL Data Sync. However, you can build a custom solution based on Sync Framework as explained here.
You can also try a product named SymmetricDS. It supports Azure SQL Database and can filter rows (using routers of type lookup, sub-select, or BSH).