Fe pública is defined as la facultad con la que están investidos determinados agentes para certificar que los hechos que les constan son verdaderos y auténticos.* I have seen fe pública translated literally as “public faith” and “public trust, renderings that admittedly don’t reflect the meaning of the expression, and as “affidavit,” a term denoting a sworn statement (declaración jurada) that may be made by any individual and not necessarily by the agents authorized to do so as in the definition above.
The act itself (el hecho de “dar fe”) has sometimes been rendered as “notarial attestation,” a possible translation if the certifying authority (fedatario público) in question is a notary public. Indeed, although most often associated with notaries, fedatario público refers to anyone authorized to ejercer la fe pública (i.e., to issue documents certifying a given event as true and authentic). Thus there is fe pública notarial, fe pública judicial, fe pública registral, fe pública administrativa, etc., and fedatarios públicos include not only notaries, but also court clerks, registrars and certain authorized civil servants. Moreover, if certification is required in a foreign country, the local Spanish consul ejerce la fe pública in his jurisdiction.
*Diccionario del español jurídico de la RAE