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 make much sense, 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.
“Notarial attestation” is also a possible translation, but only if the certifying authority (fedetario público) is a notary public. Indeed, although most often associated with notaries, fe pública 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 fedetarios 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