What is the value of a 1957 US 1 dollar silver certificate with a P at the beginning of the serial number?

1957 $1 silver certificates aren't rare. In general they're only worth about $1.50 in average condition.

The "P" at the start of the serial number doesn't help to ID the bill. Serial numbers are counters and a security feature but rarely affect a bill's value.

Some collectors will pay extra for numbers with a special pattern, e.g. 12345678, or low numbers such as 00000015.