According to Jeremiah 33:17, there shall always be an heir of King David on the throne of the house of Israel. This page traces the lineage through scripture.
Judah will reign until Shiloh comes
8 "Judah, thou art he whom thy brethren shall praise: thy hand shall be in the neck of thine enemies; thy father's children shall bow down before thee." (KJV)
9 "Judah is a lion's whelp: from the prey, my son, thou art gone up: he stooped down, he couched as a lion, and as an old lion; who shall rouse him up?" (KJV)
10 "The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be." (KJV)
11 "Binding his foal unto the vine, and his ass's colt unto the choice vine; he washed his garments in wine, and his clothes in the blood of grapes:" (KJV)
12 "His eyes shall be red with wine, and his teeth white with milk." (KJV)
David, the 8th son of Jesse
David is the 8th son of Jesse.
David, the 7th son of Jesse
13 "And Jesse begat his firstborn Eliab, and Abinadab the second, and Shimma the third," (KJV)
14 "Nethaneel the fourth, Raddai the fifth," (KJV)
15 "Ozem the sixth, David the seventh:" (KJV)
NOTE: This apparent contradiction with 1 Samuel 16:1-13 might be explained if one of Jesse's sons died before having any children and/or before making any significant contribution.
No one from the line of Conaih will ever be king of Israel.
28 "Is this man Coniah a despised broken idol? is he a vessel wherein is no pleasure? wherefore are they cast out, he and his seed, and are cast into a land which they know not?" (KJV)
29 "O earth, earth, earth, hear the word of the LORD." (KJV)
30 "Thus saith the LORD, Write ye this man childless, a man that shall not prosper in his days: for no man of his seed shall prosper, sitting upon the throne of David, and ruling any more in Judah." (KJV)
The Jews believe this is evidence that YAHSHUA is not the Messiah. I think this man is listed in the New Testament/B'rit Chadasha lineage of the Messiah.
There will always be someone from the line of David on the throne of the house of Israel.
17 "For thus saith the LORD; David shall never want a man to sit upon the throne of the house of Israel; " (KJV)