From an unused root meaning to curb; a bit -- bit, bridle.
H4964. metheg
מֶ֫תֶג noun masculine bridle (Aramaic (ᵑ7) מִתְגָּא; Late Hebrew מֶתֶג of secondary accent ָֽ; מִתֵּג Pi`el denominative put on a bridle); —
1 literally bridle, for animals; לַחֲמוֺר מֶתֶג Proverbs 26:3 a whip for the horse, a bridle for the ass, etc.; ׳בְּמ וָרֶסֶן Psalm 32:9 with bridle and halter (on text of verse compare Che); of ׳י's birdle for Sennach. (under figure of beast), בִּשְׂפָתֶיךָ וּמִתְגִּי 2 Kings 19:28 and I will put (וְשַׂמְתִּי) my hook in thy nose and my bridle in thy lips = Isaiah 37:29 (see DrIs. ed. 2, 220).
2 figurative = control, authority, only in ׳מ הָאַמָּה 2 Samuel 8:1authority of the mother city, according to MV Buhl, of especially We Dr; Bu omit as corrupt (see I. אַמָּה, above); see, further, HPS.
מְתוּשֶׁ֫לַח מְתוּשָׁאֵל, see below מַת above