i have a private network having 3 nodes, two are mining and one is listener. All three nodes are connected as peers. Now, is there any way where both miners pass same transaction at same time.
Whether your signed transaction comes from a client connected to node1, a client connected to node2, or on the network from node1 to node2, if it is the same hash and binary content, for all practical purposes it is the same transaction. The nodes do not keep duplicates in their transaction pool, so they will just say "yep, seen this one already".
Think about it, in a gossip network like Ethereum, a new transaction may come to your node from multiple peers at different times. This is a natural occurrence.
Now, did you mean "mine" the tx at the same time on 2 different blocks? Well, this is what we call a soft fork, and in practice, a node wins, eventually. You can find literature about it.