Clifton Emahaiser coined the term “Ephraim Scepter”. This was done to ridicule the concept that Joseph was the ancestor of Christ. While Joshua was never crowned as a King of Israel, in fact he led the House of Israel and the House of Judah which was the de facto "mixed multitude" across the Jordan River and into the Promised Land. Joshua assigned all of the inheritances with Judah being told in no uncertain terms to abide (Jos 18:5) in the South and Israel in the North. It should not need to be stated that when the House of Israel wanted a King that Yahweh agreed stating that a King was a rejection of him and not of Samuel (1 Sam 8:7).
Jos 1:3 -- Every place that the sole of your foot shall tread upon, that have I given unto you, as I said unto Moses.
Jos 1:4 -- From the wilderness and this Lebanon even unto the great river, the river Euphrates, all the land of the Hittites, and unto the great sea toward the going down of the sun, shall be your coast.
Jos 1:5 -- There shall not any man be able to stand (H3320) before (H6440 - face) thee all the days of thy life: as I was with Moses, so I will be with thee: I will not fail thee, nor forsake thee.
Jos 1:6 -- Be strong and of a good courage: for unto this people shalt thou divide for an inheritance the land, which I sware unto their fathers to give them.
Here Joshua was acting as Yahweh's personal agent and given unreserved power over the entire House of Israel and the mixed multitude Judah.
Jos 1:9 -- Have not I commanded thee? Be strong and of a good courage; be not afraid, neither be thou dismayed: for the LORD thy God (H430 - elohiym) is with thee whithersoever thou goest.
Here Joshua is clearly given power which can be interpreted as the scepter.
Jos 1:10 -- Then Joshua commanded (H6680) the officers of the people, saying,
Jos 1:11 -- Pass through the host, and command (H6680) the people, saying, Prepare you victuals; for within three days ye shall pass over this Jordan, to go in to possess the land, which the LORD your God giveth you to possess it.
Verse 11 was a clear mandate (scepter) from Joshua to all of the people.
Jos 1:16 -- And they answered Joshua, saying, All that thou commandest (H6680) us we will do, and whithersoever thou sendest us, we will go.
The people all knew that Joshua had the scepter without any doubt.
Jos 1:17 -- According as we hearkened (H8085 - listen, obey) unto Moses in all things, so will we hearken unto thee: only the LORD thy God be with thee, as he was with Moses.
Jos 1:18 -- Whosoever he be that doth rebel against thy commandment, and will not hearken unto thy words in all that thou commandest him, he shall be put to death: only be strong and of a good courage.
Here in the clearest and repetitive of terms, power (scepter) unto death is given to Joshua, the son of Nun, an Ephrathite. We need again to note that Joshua was magnified starting in Jos 3:7 and being completed in Jos 4:14, once all of the people had crossed the Jordan. Tell me where Judah or any of his descendants ever did anything worthy let alone being magnified?
When Christ comes in his majesty, Christ will have both the scepter and the birthright. Jew-Judah's present possession of the scepter will have been terminated.