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S BishalS Bishal 

User A has membership of two different queues named 'Queue1' and 'Queue2. They have different Routing Configuration. And also consider both queue can accept case. Now,if any case comes through omni-channel then under which queue the case will be pushed ??

SwethaSwetha (Salesforce Developers) 
HI Bishal,
This depends on the routing model & routing priority on the configurations.Thanks

Related:
https://help.salesforce.com/articleView?id=service_presence_routing_configuration_settings.htm&type=5

https://help.salesforce.com/articleView?id=omnichannel_secondary_routing_priority.htm&type=5