While it was illegal to own white people as slaves, "white" was a legal status decided in the courts. Whiteness was determined based on either common knowledge - whether someone was known in the community as white - or pseudoscientific evidence based on ancestral origin. There were occasionally, however, enslaved people who looked white - usually the offspring of white male slaveholders and their black female slaves. White slaveowners showed "special interest" in mixed-race/mulatto slaves: they were often bought and sold at higher prices, and mixed-race women were often marketed as sex slaves.

Images of "white" slaves were also used by northern abolitionists to advocate against slavery. Abolitionists claimed that Southern slaveholders were so enamored with the power and wealth afforded them by slaves that they were willing to degrade their own children. For more information, see “As White As Their Masters”: Visualizing the Color Line by Carol Goodman.

See also:

White by Law: The Legal Construction of Race by Ian Haney Lόpez

Between Black and White: Attitudes Toward Southern Mulattoes, 1830-1861 by Robert Brent Toplin

No, it was not possible to own a white person as a slave in the United States. There's plenty more on this in our FAQ, but several of the now-removed comments attempt to answer this by talking about indentured servitude -- while indentured servitude is a form of unfree labor, like slavery, it is not in fact comparable to chattel slavery (the indentured servant had rights under law, was not born into a state of servitude, and the state of servitude was time-limited).

As mentioned by my esteemed colleague u/jschooltiger, no there were not^1. Looking at my home state of Virginia, which really started to define American slavery in the late 17th century with the other colonies following her lead, we can see they made sure of that.

We (hopefully?) all now know that in the late summer/fall of 1619 two Dutch ships traded cargo in Virginia that they had raided from a ship in the Caribbean, the first transaction being about 20 humans from the Kingdom of Ndongo. While they weren't the first humans in bondage in future America, Africans in America, enslaved Africans in America, etc, etc, the Englishmen really didn't know what to do with the humans traded for "victuals" as race slavery was not yet a thing. Religion slavery was, and those without knowledge of Christ were up for grabs as enlaveable humans, legally speaking, but it really didn't have much to do with race directly and there were no colonial (or english) laws at that time really dealing with (allowing) enslavement. Indentured servants were a thing, of course, and a ready population of poor whites could be shipped from England. With the life expectancy of an indenture (or any colonist, really) being very short, indentures were far preferable to enslavement anyway as it was cost effective. As the colony became established, that began to change and before too long people didn't just die after a couple of years, and the "progress" seen in Bermuda provided a roadmap for forced labor slavery. Now people indentured actually exited their terms at their conclusion, were granted land, and the owner of the contract had to give them their rights, meaning a little clothes, food, tools, etc to get them started in life. If they'd stay alive, the more expensive "life indenture" servants would be much better economically speaking, so in the 1660s they began to really codify the laws. This started the humans are/aren't property debate as well, which continued until 1865 and the legislation provided by the conclusion of the Civil War.

One of the first things they had to tackle was what happens when a white man has a child with a black woman. "Bastards" by law were to be supported by the father, financially, and the emerging planter gentry really didn't want to have to take care (or admit the connection to) children from their life indentures (enslaved humans). So we dug up an old law concerning livestock which defines that if two animals succesfully do the deed, the offspring is property of the owner of the female animal (this legal concept is known as partus sequitur ventrem or "birth follows the womb"). It later became defined as the "one drop rule" which I'll get to some famous examples that speak to your question later, but in 1662 they passed a law stating (I've modernized the original grammer used but have not added or removed any words);

WHEREAS some doubts have arrisen whether children got by any Englishman upon a negro woman should be slave or free, Be it therefore enacted and declared by this present grand assembly, that all children born in this country shall be held bond or free only according to the condition of the mother, And that if any christian shall committ fornication with a negro man or woman, he or she so offending shall pay double the fines imposed by the former act.

Next religion had to be removed from the equation in response to several enslaved Africans challenging in court their right to freedom by having been baptised. This one really provided a conundrum because the whole justification for enslavement of "heathens" was to bring them the glory of God and allow for their soul's eternal salvation. Depriving them of that wasn't gonna work, and freeing someone you purchased wasn't gonna work, either, as an indenture that would make but at a higher price. So, in 1667, we passed a law stating that baptism was not enough to raise you from the station of slave - your reward, due to your heathen ancestry in Africa (or wherever), would have to come in the next life and not this one. The text, again modernized, reads;

WHEREAS some doubts have risen whether children that are slaves by birth, and by the charity and piety of their owners made pertakers of the blessed sacrament of baptism, should by virtue of their baptism be made free; It is enacted and declared by this grand assembly, and the authority thereof, that the conferring of baptism doth not alter the condition of the person as to his bondage or freedom; that diverse masters, freed from this doubt, may more carefully endeavour the propagation of christianity by permitting children, though slaves, or those of growth if capable to be admitted to that sacrament.

At this point we've made a law permitting slavery, defining the path of "masters" children, and taken religion out of slavery (as well as some other ones), so we really start to see "slavery" as we think of the term establishing itself. It only took two years to attach the next part, passing in 1669;

WHEREAS the only law in force for the punishment of refreactory servants (a) resisting their master, mistress or overseer cannot be inflicted upon negroes, nor the obstinacy of many of them by other then violent means suppressed, Be it enacted and declared by this grand assembly, if any slave resist his master (or other by his masters order correcting him) and by the extremity of the correction should chance to die, that his death shall not be accompted felony, but the master (or that other person appointed by the master to punish him) be acquit from molestation, since it cannot be presumed that prepensed malice (which alone makes murder felony) should induce any man to destroy his own estate.

In other words, no way would you intentionally destroy your own crops, but you may damage a few in caring for them as a whole. Same with your humans; no person would willfully kill them but may, undoubtedly unintentionally, do so in the course of discipline. As this could not possibly be intentional murder, it could not be treated as such. Except, obviously, thats a big loop hole that literally makes it a matter of small regard to kill a human bacause you "own" them.

1680;

[I]t shall not be lawfull for any negroe or other slave to carry or arm himself with any club, staff, gun, sword or any other weapon of defence or offence, nor to go or depart from of his masters ground without a certificate from his master, mistress or overseer, and such permission not to be granted but upon perticuler and necessary occasions... And it is further enacted by the authority aforesaid that if any negroe or other slave shall presume or lift up his hand in opposition against any christian, shall for every such offence, upon due proof made thereof by the oath of the party before a magistrate, have and receive thirty lashed on his bare back well laid on. And it is hereby further enacted by the authority aforesaid that if any negroe or other slave shall absent himself from his masters service and lye hid and lurking in obscure places, comitting injuries to the inhabitants, and shall resist any person or persons that shalby any lawfull authority be imployed to apprehend and take the said negroe, that then in case of such resistance, it shall be lawfull for such person or persons to kill the said negroe or slave so lying out and resisting, and that this law be once every six months published at the respective county courts and parish churches within this colony.

Two years later, in 1682 as things really start to spiral they slapped a bunch of it together and further cemented that race equals station;

Act I. It is enacted that all servants. . . which shall be imported into this country either by sea or by land, whether Negroes, Moors, mulattoes or Indians who and whose parentage and native countries are not Christian at the time of their first purchase by some Christian. . . and all Indians, which shall be sold by our neighboring Indians, or any other trafficing with us for slaves, are hereby adjudged, deemed and taken to be slaves to all intents and purposes any law, usage, or custom to the contrary notwithstanding.

XIX. And for a further prevention of that abominable mixture and spurious issue, which hereafter may increase in this her majesty's colony and dominion, as well by English, and other white men and women intermarrying with negros or mulattos, as by their unlawful coition with them, Be it enacted, by the authority aforesaid, and it is hereby enacted, That whatsoever English, or other white man or woman, being free, shall intemarry with a negro or mulatto man or woman, bond or free, shall, by judgment of the county court, be committed to prison, and there remain, during the space of six months, without bail or mainprize; and shall forfeit and pay ten pounds current money of Virginia, to the use of the parish, as aforesaid.

XXXIV. And if any slave resist his master, or owner, or other person, by his or her order, correcting such slave, and shall happen to be killed in such correction, it shall not be accounted felony; but the master, owner, and every such other person so giving correction, shall be free and acquit of all punishment and accusation for the same, as if such accident had never happened: And also, if any negro, mulatto, or Indian, bond or free, shall at any time, lift his or her hand, in oppostion against any christian, not being negro, mulatto, or Indian, he or she so offending, shall, for every such offence, proved by the oath of the party, receive on his or her bare back, thirty lashes, well laid on; cognizable by a justice of the peace for that county wherein such offence shall be committed.

Cont'd

I have a followup question: I've been told that during Cromwell's era certain Scottish prisoners were transported to Jamaica - as slaves - and further, I have met Jamaican people who are black and claim to be the descendants of those slaves.

The argument was that the slaves in question were captured in military engagement and enslaved alongside black slaves and being that there were no white women, they married and had children with black ones.

Is there any evidence of this at all?