I have been exploring bitcoin API and I found there is network fee for every transaction which is around 0.0001 but I noticed many trading and bitcoin related agencies doesn't charge any network fee at all for transfer between user on same Website/App. Few of which are cryptopia, Zebpay and localbitcoins.
Could someone help me understand that how they are able to transfer between wallet without any network fee.
Organizations that offer online wallets aren't obligated to handle transactions using the actual Bitcoin blockchain; they may instead choose to keep their own off-chain record of transactions between users. While faster and cheaper than on-chain transactions, this system is often less secure, especially since the transaction records are centralized.
Only when a user transfers Bitcoins between an external wallet would an organization utilize the blockchain; this is when a transfer would cost some network fee and take some time to process.