Christopher Smith migrated from England to New England.
Vol I Page 286 and 744 does not list Alice as a child of this couple.
From "List of One Hundred and Fifteen Colonial Ancestors."
Eighth in descent from Christopher Smith (...-1676).
Deputy to the General Court of Massachusetts, 1655.
Chosen sergeant at Providence, Rhode Island, 1655.
Need to get this book: CS71.S643 2003 Ancestry & descendants of Judge Rufus Biggs Smith 1854-1923: a descendant of Immigrant Christopher Smith of Providence, RI by Harrison Black
New England Families, Genealogical and Memorial By William Richard Cutter Vol. 1 p 474
Christopher Smith, a member of the Society of Friends in Providence, who died in June 1676, in Newport, having removed to that town for safety during the Indian wars, with many others in the outlying districts of Providence. He was taxed 3 shillings and 4 pence in Providence, September 2, 1650, was a freeman, April 27, 1655, and juryman in the same year. He was granted a share of the meadows, March 16, 1656, to be laid out in the meadows called "World's End, "in lieu of a share formerly laid out to him beyond the great meadow. He took up sixty acres of land and a share in the meadows, July 7. 1658, and in a division of lands, February 19, 1665, he drew lot No. 25. He subscribed to the oath of allegiance, June I, 1667. He sold twenty acres of land, August 21, 1660, and another parcel, November 28, 1672. His wife Alice survived him by about five years, dying in 1681. Children: Susanna, died 1692; Thomas, mentioned below; Benjamin, born 1631, died December 23, 1713.
"A History of the Episcopal Church in Narragansett, Rhode Island" By Wilkins Updike, James MacSparran, 2nd edition, 1907 "Christopher Smith." Vol I p. 579
"The date of Christopher Smith's birth is not known. He first appeared upon the records in Providence, September 2, 1650, when he was taxed 3s.4d. He was granted or took up several tracts of land, and married a wife named Alice, having by her four children, of whom Susannah, who became Mrs. Lawrence Wilkinson, was the eldest. At the time of the breaking out of King Philip's War, Mr. Smith took refuge in Newport, dying there soon afterward, in June 1676. He is called, inthe Friends' records of that town, "an ancient Friend of Providence." "
CHRISTOPHER, Providence, in the list of freem. there 1655, had d. Susanna wh. m. Lawrence Wilkinson; engag. for alleg. to Charles II. June 1668. In 1672, his w. was Alice; but what was her fam. name, or whether she was first, sec. or later w. is unkn.
"Christopher Smith, immigrant ancestor, and progenitor was a native of England, whence he came to the American colonies at a date unknown. He is first of record in Providence on September 2, 1650, when he was taxed three shillings, fourpence. In 1655 he was admitted a freeman, and on April 27 of the same year served as a juryman. On March 16, 1656, he was granted a share of meadow to be laid out beyond the meadow called World's End, in lieu of a share formerly laid out to him beyond Great Meadow and Pawtuxet Path. On July 27, 1658, he took up sixty acres and a share of the meadow. On February 19, 1665, he drew Lot 65 in a division of lands. On June 1, 1667, he subscribed to the oath of allegiance. On August 21, 1668, he and his wife, Alice, sold Asten Thomas twenty acres. On November 28, 1672, he and his wife sold to Shadrach Manton a parcel of lowland. Christopher Smith went to Newport at the outbreak of King Philip's War, and died there in June 1676, as declared by the records of the Society of Friends, which call him an ancient Friend of Providence. The surname of his wife, Alice, is not known."
The earliest mention of Christoper in the Providence records was 3rd 9th month 1649 when he was one of six who might, by lot, receive Mris Lea’s lot. 
Christopher was a juror in 1652, 1655 and 1656. He volunteered “to ye good example of all younger Persons” to help the constable return a prisoner to the constable at Secunck
Christopher swore his allegiance to King Charles II, 30 May 1667 and was on a list of freeman 4 May 1669 although he had, evidently, been a freeman a long time before that.
There are many land transactions in his name in the Providence records. He received grants, bought, sold and traded property. He signed his name to many of the deeds. Alice his wife made a mark.
There were 19 men on a June 1652 rate list. Christopher and 4 others paid the second to top rate of L1. 10.00. Most of the list paid 4s.0d. June 1671, he paid a rate of 5s, his son Edward paid 10s.
In 1676, Christopher and Alice’s house was burned down by Indians. He is believed to have evacuated to Newport prior to the attack. He died there within a few months
"SMITH Christopher, an "ancient Friend," Providence, died at Newport, June -, 1676."
Gravesite is unknown but said to be in Newport, Rhode Island. 
Officials from the Newport Historical Society state:
"Smith's burial is only known through the Friends records..." and ..."there is no physical evidence of it that I've been able to find."
"If Smith was buried in Newport, the two Friends burying grounds that he could have been interred in are Clifton/Golden Hill and Friends. He could also have been buried in the Common Ground or perhaps in the family burying ground of a friend. If he was a Quaker his grave was probably either unmarked or marked with a simple fieldstone."
"There is no day of the month in the Quaker records. His burial place is not known and there were no local stone cutters in Newport at that time."
Religion and church excommunication
He may have been a Seeker, but he later became a Quaker and relocated to the religious freedom offered in Providence, Rhode Island. In August 1625, he was accused of adultery and removed from his church position in Stratford Upon Avon. My assumption is that the church wanted this free-thinker out of their church. This email from Bob Bearman in Stratford Upon Avon is the only documentation I have on this episode (Cooper-1 14:10, 10 June 2017 (EDT)):
At this hall the company, upon taking into consideration that Christopher Smith hath much wronged this company & disgraced them, not only by his heinous offense in committing adultery but also in that he hath refused to be censured by the judge of our peculiar jurisdiction, appealing to the court of Worcester thereby weakening our liberties of this borough, as we conceive it, contrary to his duty, wherefore they have removed him from the place of a principle burgess and service in this place and for that he standeth excommunicate and will not submit himself to the law.
Council Book B, 7 September 1625.
From that email, "The ‘peculiar jurisdiction’ is a reference to the Stratford-upon-Avon church court, whose authority Smith refused to recognize. Instead, he appealed to the bishop’s court at Worcester (Stratford was in the Worcester diocese). He had been chosen a capital burgess on 18 April 1623. Earlier he had been aletaster (1617) and then one of the constables (1618-19). He was also churchwarden, from 1623 to 1625."
Immigrant Ancestor of yDNA group NE18 father Christopher Smith (c1591 ENG-1676 Newport, Rhode Island) m Alice Gibbes on SmithConnections Northeastern DNA Project.
↑ Cadle, Harriet Swan. List of one hundred and fifteen colonial ancestors of Cornelius Cadle : Muscatine, Iowa, member Missouri Society of Colonial Wars
Muscatine, Ia. Mrs. Charles Francis Cadle, c 1909.
↑ Savage, James. A Genealogical Dictionary of the First Settlers of New England Showing Three Generations of Those Who Came Before May 1692. Vol. I-IV. Boston, MA, USA: 1860-1862. Vol. IV p. 111
↑ Smith and Sanborn cite Correspondence of Roger Williams 2:721
↑ (Town Page Detail: Monthly Meeting 1676 Providence, Rhode Island, United States)
↑ Arnold, James N.. Vital record of Rhode Island, 1636-1850, first series, births, marriages and deaths : a family register for the people. Vol VII. "Friends and Ministers." Providence, R.I.: Narraganset Historical Publishing Co., 1891-1912. p. 121 Accessible at Ancestry.com ($)
↑Seekers on Wikipedia The Seekers, or Legatine-Arians as they were sometimes known, were an English Protestant dissenting group that emerged around the 1620s, probably inspired by the preaching of three brothers – Walter, Thomas, and Bartholomew Legate. Seekers considered all organised churches of their day corrupt and preferred to wait for God's revelation. Many of them subsequently joined the Religious Society of Friends (Quakers).
The Register of Stratford on Avon page 28 marriage record. Christopher and Alis married on May 1, 1616. This was in the same church where just a few days earlier William Shakespeare was buried in the chancel (of the Holy Trinity Church) two days after his death on 23 April 1616.
Colket, Jr., Meredith B. 1912-. Founders of Early American Families: Emigrants From Europe, 1607-1657, Revised Edition. Cleveland: General Court of the Order of Founders and Patriots of America: distributed by Founders Project, 1985. Text located at the New England Historical and Genealogical Society library. Search results for "Christopher Smith"
Rhode Island: Vital Records, 1636-1850. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2014), Originally Published as Vital record of Rhode Island 1636-1850: First Series: births, marriages, and deaths: a family register for the people, by James N. Arnold. Providence, RI: Narragansett Historical Publishing Company. V7, p. 121. [See Also: Rhode Island Monthly Meeting- Deaths. (Book # 822 p. 4)]
There are several Smiths that were members of the Holy Trinity Church in Stratford-Upon-Avon in the late 1500s. It is strictly a guess, but I wonder if William Smith that married Elizabeth Comton alis Symys on May 15, 1585 might be Christopher's parents. This guess is only based on the timing of his birth c1591 and that Christopher named his firstborn William. More research needed. The registers of Stratford-on Avon, in the county of Warwick, page 12
It may be possible to confirm family relationships with Christopher by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: