From BiblePortal Wikipedia

Cyclopedia of Biblical, Theological and Ecclesiastical Literature [1]

( Βεζεθά ), the name of the fourth hill on which a part of Jerusalem was built, situated north of Antonia, from which it was separated by a deep fosse, but not enclosed till the erection of the third wall by Agrippa, according to Josephus ( War, 5:4, 2), who interprets the name as equivalent to "New City" ( Καινὴ Πόλις ), perhaps regarding it as the Hebrews חֲדָשָׁה בֵּית ; but as this can hardly be considered a representative of the name, and as Josephus elsewhere ( War, 2, 19, 4) seems expressly to distinguish Bezetha from Caenopolis or the New City ( Τήν Το Βεζεθὰν Προσαγορευομένην Καί Τὴν Καινόπολιν , unless, as Reland suggests, Palest. p. 855, we should read Τὴν Καὶ Καινόπολιν , making them identical), we may perhaps better adopt the derivation given above under the BEZETH (See Bezeth) (q.v.) of  1 Maccabees 7:19. The general position of the hill is clear; but it has been nevertheless disputed whether it should be regarded as the eminence north of the present Damascus gate (Robinson, Bibl. Res. 1, 392; Bib. Sac. 1846, p. 438 sq.) or (as is more probable) that immediately north of the present Haram enclosure (Williams, Holy City, 2, 50). (See Jerusalem).

Tristram thinks that "beyond a shadow of doubt" this hill "forms the greater part of the Mohammedan quarter of modern Jerusalem a broad, irregular ridge, separated from Moriah by the fosse and great Pool of Bethesda, from Akra by the Harmonaean valley, and with a rugged, precipitous descent on the east to the valley of Jehoshaphat or Kedron. The northern part, now a Moslem cemetery, is outside the walls" (Bible Places, p. 140).

International Standard Bible Encyclopedia [2]

be - zē´tha  : Also called by Josephus the "New City" ( BJ , V, iv, 2), certain suburbs of Jerusalem, North of the Temple, which were outside the second but included within the third wall. Bezeth (which see) may be the same place. See Jerusalem .