Pre Byzantium Transaction Status

How should I find the status of transaction(success/failed) that happened pre Byzantium in the Blockchain?

The transaction history exists pre Byzantium and is viewable from block explorers. Are you referring to a txn that was in the pending txn pool at the time of the fork?

I used infura API “getTransactionByHash” to collect transactions, but some are failed. I am not able to distinguish between the failed and successful transaction by the data retrieved from the above API, as the data do not contain gas limit and gas used. Is it possible to decide success/fail of a transaction using retrieved data?

OK, so this isn’t related to a fork. Have you also reviewed the JSON RPC spec for that method here:

Also, look at eth_getTransactionReceipt for obtaining gas information.

TransactionReceipt return status post Byzantium before that it returns the root.
Yes, their is " debug_tracetransaction" which do so but that I need to run full node geth I guess ?