"Bathsheba, Mary's And Joseph's Ancestor"

Was Jesus the son of Mary and Bathsheba by bloodline
and Joseph merely titular by the Mosaic patriarchal law?
"But after he had considered this, an angel of the Lord appeared to him
in a dream and said, 'Joseph son of David, do not be afraid
to take Mary home as your wife, because what is conceived in her is from the Holy Spirit." Matthew 1:20 NIV

Luke 3:23 Now Jesus himself was about thirty years old when he began his ministry. He was the son, so it was thought, of Joseph, the son of Heli, (and the patriarchs)
Gk. gennao, ghen-nah'-o; ...to procreate (properly of the father, but by extension of the mother); figuratively to regenerate:--bear, beget, be born....
Were David and Bathsheba ancestors of Jesus by law or by bloodline?
Luke 3:31 the son of Melea, ...the son of Mattatha, the son of Nathan, the son of David,
1 Chr 3:5 and these were the children born to (David) there: Shammua, Shobab, Nathan and Solomon. These four were by Bathsheba daughter of Ammiel.

Why did Scripture condemn David but not Bathsheba? Is part of the explanation in - - -
1 Sam 8:6 ff. But when they said, "Give us a king to lead us," this displeased Samuel; so he prayed to the LORD.... 9 Now listen to them; but warn them solemnly and let them know what the king who will reign over them will do." 16 Your menservants and maidservants and the best of your cattle and donkeys he will take for his own use. 17 He will take a tenth of your flocks, and you yourselves will become his slaves.
1 Chr 24:19 This was their appointed order of ministering when they entered the temple of the LORD, according to the regulations prescribed for them by their forefather Aaron, as the LORD, the God of Israel, had commanded him.
See Num 3:4 - 10...only Eleazar and Ithamar served as priests during the lifetime of their father Aaron. 5 The LORD said to Moses, 6 "Bring the tribe of Levi and present them to Aaron the priest to assist him. 7 They are to perform duties for him and for the whole community at the Tent of Meeting by doing the work of the tabernacle." 10 Appoint Aaron and his sons to serve as priests; anyone else who approaches the sanctuary must be put to death.
Num 4:15 "After Aaron and his sons have finished covering the holy furnishings and all the holy articles, and when the camp is ready to move, the Kohathites (Levites) are to come to do the carrying. But they must not touch the holy things or they will die. The Kohathites are to carry those things that are in the Tent of Meeting. (when the camp is ready to move)
1 Chr 23:25 For David had said, "Since the LORD, the God of Israel, has granted rest to his people and has come to dwell in Jerusalem forever, 26 the Levites no longer need to carry the tabernacle or any of the articles used in its service."
How did the Philistines capture the ark? Read 1 Sam 4:3 & 16-18.
Read 1 Samuel 6:1-8. Why did they wish to send it back? What was its transport?
But what was the instruction Moses gave the Israelites?
Exo 37:5 And (Moses) inserted the poles into the rings on the sides of the ark to carry it.
Read 2 Sam 6:1-7. If it suited our neighbors to use a new cart, why not do likewise?
1 Chr 15:15 And the Levites carried the ark of God with the poles on their shoulders, as Moses had commanded in accordance with the word of the LORD.
2 Sam 6:9-11 David was afraid of the LORD that day and said, "How can the ark of the LORD ever come to me?" 10 He was not willing to take the ark of the LORD to be with him in the City of David. Instead, he took it aside to the house of Obed-Edom the Gittite. 11 The ark of the LORD remained in the house of Obed-Edom the Gittite for three months, and the LORD blessed him and his entire household.

“When all else fails, read the instructions.” What was the proper method? Whom did Moses (God) assign?
Now read 2 Sam 6:12-14.
1 Chr 15:11-13 & 24 Then David summoned Zadok and Abiathar the priests, and U., A., J., S., E. and A. the Levites. 12 He said to them, "You are the heads of the Levitical families; you and your fellow Levites are to consecrate yourselves and bring up the ark of the LORD, the God of Israel, to the place I have prepared for it. 13 It was because you, the Levites, did not bring it up the first time that the LORD our God broke out in anger against us. We did not inquire of him about how to do it in the prescribed way."
1 Chr 15:24 S., J., N., A., Zechariah, Benaiah and Eliezer the priests were to blow trumpets before the ark of God. Obed-Edom and Jehiah were also to be doorkeepers for the ark.

Who among Obed-Edom's descendants became famous?
1 Chr 26:4 Obed-Edom also had sons: S. the firstborn, J. the second, J. the third, S. the fourth, N. the fifth, 5 Ammiel the sixth, I. the seventh and P. the eighth. (For God had blessed Obed-Edom.)
1 Chr 3:5 and these were the children born to him there: Shammua, Shobab, Nathan and Solomon. These four were by Bathsheba daughter of Ammiel.

Recall Luke's ancestral listing for Mary's father, Heli, indicates descent from Nathan, Bathsheba's son by David of Judah. (She is of the Levitical priesthood.)
Luke 1:5 (KJV) There was in the days of Herod, the king of Judaea, a certain priest named Zacharias, of the course of Abia: and his wife was of the daughters of Aaron, and her name was Elisabeth. (Of Aaronic priestly ancestry.)
Luke 1:36 KJV And, behold, thy cousin Elisabeth, she hath also conceived a son in her old age: and this is the sixth month with her, who was called barren.
Observing that Elisabeth's parents were priestly, then Mary's and Elisabeth's mothers probably are sisters (Luke pointedly mentions "daughters of Aaron" for M . & E . to be cousins while Heli is of Judah. Then Mary's maternal ancestry is priestly. Since Joseph and Heli, according to Mosaic patriarchal law, are of David the King (through brothers) and Mary, who contributed genes, is priestly in origin, then Jesus is both king and priest, i.e., paternally and maternally.