I already know American Express and Etrade transfer funds to other banks fast.
the next day. Rest of the banks take three days. Do you know of any banks
that have fast transfers between institutions?

The system works like this:

Institution 1 (source) compiles a list of all transactions for the day. This list includes the account and bank information of institution 2 (target). The list is electronically transferred to one of the Federal Reserve clearing houses. The clearing house makes a list of all the transactions for each target and transmits that to the target institution.

All this happens overnight. So the target processes the transfer generally the next day, sometimes it might be the second day. The law allows institutions 3 days.

Some institutions may have agreements to directly make the transfer without going through the clearing house to provide next day transfers.

Thanks