Why are the fee value and modified fee value always the same? I do not see any transaction in the mempool having differing values for the fee and modified fee fields. Does nobody modify or accelerate their transactions?
How do transactions with modified fees show up in the mempool?
I can not see any transaction resting in Mempool having different values for Fee and Modified Fee fields?

That's probably because you haven't modified any.
The prioritisetransaction RPC exists for miners to signal that particular transactions are paid for out of band, or are the miner's own transactions that should prioritized for block construction over what is implied by their feerate.
If you're not a miner, there is no need to ever use this RPC, and the fee and modified fee will be identical for all transactions.