How much physical currency does the Fed transfer to banks per year? I just wonder since money has to enter the system somehow. Currently the Fed will supply whatever banks ask to meet their capital needs. But how much physical currency does the Fed, treasury, and mint transfer to banks per year? And which banks?
The amount of currency in circulation (bills and coins) is published by the Federal Reserve. (Available at the FRED web site.) The annual change in this time series is the amount created.

This is the amount outstanding, it does not tell us how much currency is being destroyed and replaced. Also, there is seasonal demand for currency, and some cash is shipped back and forth.

The creation of currency is not really a "transfer" (gift). The banks need to buy the currency by exchanging reserves (settlement balance at the Fed) for the notes.

Finally, the Federal Reserve does not single out how much it deals with any particular banks by name under normal circumstances. (During some of the special operations undertaken after the Financial Crisis, the Fed published some information about their counterparties.) The most you would get would be on the basis of the category of bank.