Fausset's Bible Dictionary 
1. 1 Chronicles 6:40.
2. Ezra 10:25.
3. Ezra 10:31.
4. Nehemiah 3:14.
5. Nehemiah 3:31.
6. Nehemiah 8:4.
7. Nehemiah 11:12; Jeremiah 38:1.
8. Son of Hammelech, or "of the king" into whose dungeon Jeremiah was cast ( Jeremiah 38:6). Jerahmeel also is called "son of Hammeleeh" or "the king" ( Jeremiah 36:26), and Joash ( 1 Kings 22:26), and Maaseiah ( 2 Chronicles 28:7). Therefore the title is official, one of the royal family, exercising some of the royal prerogative.
Hawker's Poor Man's Concordance And Dictionary 
We meet with many of this name in Scripture. There was a Malchiah chief of a family in Israel. ( 1 Chronicles 24:9) See also concerning others of this name 1 Chronicles 6:40; 1Ch 9:12; Ezra 10:25; Nehemiah 3:11; Neh 3:14; Neh 3:31. And the father of Pashur was a Malchiah; as he was also the worthless character whose name is rendered memorable, in infamy, for his cruelty to God's prophet. (See Jeremiah 21:1; Jer 38:6 etc.) The name but corresponded with the actions of those men. Malchiah is a compound of Melek, a king; and Jah, the Lord; therefore Malchiah means, "the Lord rules, or the Lord is king."
Hastings' Dictionary of the Bible 
MALCHIAH. 1. A priest, the father of Pashhur ( Jeremiah 21:1; Jeremiah 38:1 ), same as Malchijah of 1 Chronicles 9:12 , Nehemiah 11:12 . Nehemiah 11:2 . A member of the royal family, to whom belonged the pit-prison into which Jeremiah was let down ( Jeremiah 38:6 ).
Easton's Bible Dictionary 
Bibliography Information Easton, Matthew George. Entry for 'Malchiah'. Easton's Bible Dictionary. https://www.studylight.org/dictionaries/eng/ebd/m/malchiah.html. 1897.
Cyclopedia of Biblical, Theological and Ecclesiastical Literature 
(Heb. Malkiyah'. מִלְכַּיָּה , and [ Jeremiah 38:6] Malkiya'Hu, מִלְכַּיָּהוּ , King Of Jehovah; Sept. Μελχία or Μελχίας , but in Nehemiah v. r. Μελχεία or Μελχείας ; Auth. Version "Malchijah," in 1 Chronicles 9:12; 1 Chronicles 24:9; Nehemiah 3:11; Nehemiah 10:3; Nehemiah 12:42; Ezra 10:25, last occurrence; "Melchiah" in Jeremiah 21:1), the name of at least ten persons near the time of the Babylonian exile.
2. The head of the fifth division of the sacerdotal order in the distribution appointed by David ( 1 Chronicles 24:9). B.C. 1014.
3. A priest, the father of Pashur ( 1 Chronicles 9:12; Nehemiah 11:12),which latter was one of those who proposed to execute the prophet Jeremiah on a charge of treason ( Jeremiah 38:1), although he had but unfavorably answered his inquiry respecting the fate of the city ( Jeremiah 21:1). B.C. ante 589. He is very possibly the same with the son of Hammelech (lit. The King'S Son ) , and owner or constructor of the private dungeon into which Jeremiah was cruelly thrown ( Jeremiah 38:6). (See Jeremiah). "The title Ben-Ham-Melek is applied to Jerahmel ( Jeremiah 36:26), who was among those commissioned by the king to take prisoners Jeremiah and Baruch; to Joash, who appears to have held an office inferior to that of the governor of the city, and to whose custody Micaiah was committed by Ahab ( 1 Kings 22:26); and to Maaseiah, who was slain by Zichri, the Ephraimite, in the invasion of Judah by Pekah, in the reign of Ahaz ( 2 Chronicles 28:7). It would seem from these passages that the title ‘ king's son' was official, like that of ‘ king's mother,' and applied to one of the royal family, who exercised functions somewhat similar to those of Potiphar in the court of Pharaohs"
4. One of the Israelites, former residents (or descendants) of Parosh, who divorced his Gentile wife after the exile ( Ezra 10:25). B.C. 459.
5. Another Israelite of the same place (or parentage) who did likewise ( Ezra 10:25). B.C. 459. In the Sept. (ad loc. and 1 Esdras 9:26) his name appears as Ἀσυβίας . 6. One of the former residents (or descendants) of Harim, who assisted in reconstructing the wall of Jerusalem after the return from Babylon ( Nehemiah 3:11). B.C. 446. He was one of the Israelites who had previously divorced his (Gentile wife ( Ezra 10:31). B.C. 459.
7. Son of Rechab, and ruler of part of Beth-haccerem, who repaired the dung-gate of Jerusalem after the captivity ( Nehemiah 3:14). B.C. 446.
8. The son of a "goldsmith," and the repairer of part of the wall of Jerusalem opposite Ophel ( Nehemiah 3:31). B.C. 446.
9. One of the priests appointed as musicians, apparently vocal, to celebrate the completion of the walls of Jerusalem after the exile ( Nehemiah 12:42). B.C. 446.
10. One of those who supported Ezra on the left hand while reading the law to the people assembled at Jerusalem ( Nehemiah 8:4); probably the same with one of the priests who subscribed the sacred covenant entered into on the same occasion ( Nehemiah 10:3). B.C. cir. 410.