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Would like to get your take on Calvin’s case.

Calvin's Case (1608) decided that children born of Scots after the 1603 accession of James I to the throne were natural born subjects of the king. The sitting judge was Lord Ellsemere. Lord Coke was among the fourteen judges who decided the case. Calvin was born in Scotland November 1605.

Calvin's Case is the genesis for jus soli, the English common law of birthright citizenship due to place of birth. The United States recognizes both jus soli, and jus sanguinis, law of blood, or inherited citizenship.

Calvin's Case 7 Coke Report 1a, 77 ER 377

Case of the postnati.

Black's Law Dictionary, 11th Ed.

postnatus. [Latin] (17c) A person born after a certain political event that affected tyhe person's political rights; esp., a person forn after the Declaration of Independence. Cf. Antenatur. Pl. postnati.
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Calvin's case. (17c) The decision establishing that persons born in Scotland after the 1603 accession of James 1 to the English throne were deemed natural-born subjects of the King of England and could inherit English land. Calvin v. Smith, 7 Eng. Rep. 1, 2 S.T. 559 (1608)

7 Coke Report 6b, 77 ER p384

3. Concerning the local obedience it is observable, that as there on the King's part, so there is a (d) local ligeance of the subject's part. And this appeareth in 4 Mar. Br. 32. (e) and 3 and 4 Phil. and Mar. Dyer 144. Sherley a Frenchman, being in amity with the King, came into England, and joined with divers subjects of this realm in treason against the King and Queen, a concluded (f) contraligeant' suae debitum; for he owed to the King local obedience, that is, so long as he was within the King's protection; which local obedience being but momentary and uncertain, is yet strong enough to make a natural subject; for if he hath issue here, that issue is (g) a natural born subject; a fortiori he that is born under the natural and absolute ligeance of the King (which, as it hath been said alta ligeantia) as the plaintiff in the case in question was, ought to be a natural born subject; for localis ligeantia, est ligeantia intima et minima, et maxima incerta. And it is to be observed, that it is nec caelum, nec solum, neither the climate nor the soil, but ligeantia and obedientia that make the subject born; for if enemies come into the realm, and possess town or fort, and have issue there, that issue is no subject to the King of England, though he be born upon his soil, and under his meridian, for that he was not born under the ligeance of a subject, nor under the protection of the King.

A Frenchman who enters Britain and joins in treason against the British crown, should he have a child in Britain, the child is a natural born subject, in accordance with the explicit wording of Sir Edward Coke regarding Calvin's Case.

However, if Barack Obama's father had been part of an invading army that had captured Hawaii, and was there when Hawaii was being held as occupied territory not under the control of the United States, and baby Barack was born in said occupied territory to a member of the invading force, that would not have conferred natural born citizenship pursuant to jus soli.

English Reports, Volume CXLV, 145 E.R. 223

CASE LXXXII. 6 Jac. 7 Co. 1, Calvin's case. Alien, Denizen. 7 Co. 18 b. 27, 2 Vent. 6. See concerning Aliens, the statutes following. 11 and 12 W. 3, cap. 6. 12 W. 3, cap. 2. 7 Annæ , cap. 5. 1 G. 1 , cap. 4. 5 G. 1 , cap. 27. 4 G. 2.
[S. C. 7 Co. Rep. 1; 77 E. R. 377 (with note).]
A Scot born after the death of Queen Elizabeth, is a leigeman of England: otherwise of a Scot born before: for after the death of Queen Elizabeth, the English and Scots became subjects to one King; and their birth being under the allegiance of one King, is all one with those of Wales and Ireland. Calvin postnatus in Scotland brought an assise of lands in Middlesex; and it was pleaded to his person, that he was an alien born in Scotland, after the death of Queen Elizabeth sub ligeantia Regis Scotiæ; there was a demurrer upon this plea; it was adjourned several terms: at last it was resolved for the plaintiff by all the judges of England; and only a respondent ouster against the defendant, and not peremptory; although it was adjourned, as aforesaid.
A Scot antenatus has a son born in England; this antenatus is made a denizen; and purchases land in fee, and dies; this land does not descend to his son: for the said son was not born before the denization of the father. So of every other alien. But of a son born after the denization, the law is otherwise: for the denization gives him English blood as to the issue born afterwards only. It is otherwise of naturalization.
If a demurrer is joined upon a plea to the jurisdiction, person, writ, upon view, aid, voucher, essoin; although it be adjourned to another term, and judged against the defendant who pleads such plea; it is only a respondeat ouster. If the plea to the writ, upon issue joined, be found for the tenant or defendant, the writ shall abate. If to the person, action, or jurisdiction, and it be found for the demandant or plaintiff, he shall recover the thing in demand.' Upon a counterplea of view, resceit, essoin, or aid; and found for the tenant upon issue joined; the writ shall not abate: but view, resceit, essoin, aid prayer shall only be awarded. Upon a counterplea of voucher, if it be found for the tenant upon issue joined; the judgment shall be, that the voucher shall stand: if for the [307] demandant; the demandant shall recover the land: and it is so ordained by West. 1, cap. 39. 7 H. 6, 41. 7 H. 6, 41. 15 E. 4. Fitz. Assise, 33. 36 Ass. pl. 6. Where the view, essoin, aid or resceit are demanded; and it is found for them upon a counter-plea; the demandant is only delayed; and this delay is sufficient punishment for him; and the writ is admitted good, and shall not abate. Upon a counterplea of voucher where it is found for the demandant; he shall recover the land: for it is so ordained by the said statute. In case of a plea to the writ, person or action, found for the defendant or tenant; the defendant or tenant is unjustly troubled; and therefore the writ ought to abate. The law presumes greater delay and expence upon a trial by a jury, than upon demurrers; if upon any of those pleas there be a trial by a jury, and it be found for the demandant; he shall recover the land.

https://en.wikipedia.org/wiki/Calvin%27s_Case

Postnati and antenati
James, King of Scots, inherited the throne of England in 1603, uniting both kingdoms under a single monarch.
The decision in Calvin's Case hinged on Calvin's status as one of the postnati—subjects born into the allegiance of the Scottish king James after he had become the king of England in 1603—and on the fact that the monarch into whose allegiance he was born (the same James, in his capacity as King of Scots) was also the English king at the time of Calvin's birth—meaning that Robert Calvin, in the judgement of the court, was just as much a subject of the king of England as if he had been born in England instead of Scotland. The judges of the court cited existing statutes—including particularly a 1351 statute, De Natis Ultra Mare, which granted the benefits of subject status to foreign-born children of the king's subjects—as supporting the concept that allegiance was tied to the person of the king, rather than to the kingdom itself or its laws.
Calvin's Case did not extend English subject status to the antenati (Scots born prior to 1603). They remained aliens in relation to England, on the theory that King James had not yet become the king of England at the time of their birth. Attempts had been made in the English Parliament, prior to Calvin's Case, to naturalise all of James's Scottish subjects—both those born after his English accession in 1603 (the postnati) and also those born before 1603 (the antenati)—but these legislative efforts had been unsuccessful.[ Concerns had been expressed that extending the privileges of English subjects to all Scots would cause England to be flooded by "an influx of 'hungry Scots'". Objections were also raised that granting naturalisation to all the Scots would have encouraged the legal philosophy, espoused by James, of absolute monarchy and the divine right of kings. Even after Calvin's Case, the English Parliament could have enacted a naturalisation bill covering the antenati, but it never did so.
Later influence
Calvin's Case contributed to the concept of the Rights of Englishmen. Some scholars believed that the case did not fit America's situation, and thus reasoned that the 18th century colonists could "claim all the rights and protections of English citizenship." In fact, one scholar asserts that the legal apologists for the American Revolution claimed they had "improved on the rights of Englishmen" by creating additional, purely American rights.
Owing to its inclusion in the standard legal treatises of the nineteenth century (compiled by Edward Coke, William Blackstone, and James Kent), Calvin's Case was well known in the early judicial history of the United States. Consideration of the case by the United States Supreme Court and by state courts transformed it into a rule regarding American citizenship and solidified the concept of jus soli as the primary determining factor controlling the acquisition of citizenship by birth. The case has also been cited as providing legal justification for the restriction of legal rights to Native Americans following their conquest and confinement in reservations by the federal government of the United States.

http://www.uniset.ca/naty/maternity/9YJLH73.htm

See also Polly J. Price, NATURAL LAW AND BIRTHRIGHT CITIZENSHIP IN CALVIN'S CASE (1608), 9 YALE J.L. & HUMAN. 73 (1997)

To be clear what common law is, the definition in Black's Law Dictionary, 6th Ed. follows. Written law takes precedent over common law. Any common law inconsistent with the Constitution and any statute law is inapplicable.

Common law. As distinguished from statutory law created by the enactment of legislatures, the common law comprises the body of those principles and rules of action, relating to the government and security of persons and property, which derive their authority solely from usages and customs of immemorial antiquity, or from the judgments and decrees of the courts recognizing, affirming, and enforcing such usages and customs; and, in this sense, particularly the ancient unwritten law of England. In general, it is a body of law that develops and derives through judicial decisions, as distinguished from legislative enactments. The "common law" is all the statutory and case law background of England and the American colonies before the American revolution. People v. Rehman, 253 C.A.2d 119, 61 Cal. Rptr. 65, 85. It consists of those principles, usage and rules of action applicable to government and security of persons and property which do not rest for their authority upon any express and positive declaration of the will of the legislature. Bishop v. U. S., D.C.Tex., 334 F.Supp. 415, 418.
As distinguished from ecclesiastical law, it is the system of jurisprudence administered by the purely secular tribunals.
Calif. Civil Code, Section 22.2, provides that the "common law of England, so far as it is not repugnant to or inconsistent with the Constitution of the United States, or the Constitution or laws of this State, is the rule of decision in all the courts of this State."
In a broad sense, "common law" may designate all that part of the positive law, juristic theory, and ancient custom of any state or nation which is of general and universal application, thus marking off special or local rules or customs.

To any who may consider that the Law of Nations in any way governs domestic citizenship determinations of the United States (or anywhere else), it is useful to know what the Law of Nations is.

Black's Law Dictionary, 6th Ed.

Law of nations. See International law.

Law of Nations is just the gone out of fashion term for International Law. Domestic citizenship determinations in the United States are governed by United States law, not international law.