To trigger this quest, you will have to complete The Nuclear Option Railroad quest and pursue a number of Radiant quests for various members of The Railroad. Eventually, P.A.M. will ask you to hunt down one of the very few Veritbirds left after the destruction of the Prydwen airship.
As this is a Radiant quest, the designated location will be random. Wherever it is, head there to take down the Vertibird. Once destroyed, report back to P.A.M. to complete the quest.